Michael Freedman | Academic Influence

Michael Freedman's AcademicInfluence.com Rankings

Michael Freedman

Mathematics

#103

World Rank

#272

Historical Rank

#39

USA Rank

Measure Theory

#694

World Rank

#941

Historical Rank

#278

USA Rank

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Mathematics

Michael Freedman's Degrees

PhD Mathematics Princeton University

Why Is Michael Freedman Influential?

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According to Wikipedia, Michael Hartley Freedman is an American mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic ℝ4 manifold exists.

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Michael Freedman's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Non-Abelian Anyons and Topological Quantum Computation (2007) (3867)
The topology of four-dimensional manifolds (1982) (1394)
Topology of 4-manifolds (1990) (1082)
Majorana zero modes and topological quantum computation (2015) (718)
A Modular Functor Which is Universal¶for Quantum Computation (2000) (442)
Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes (2016) (412)
Topologically protected qubits from a possible non-Abelian fractional quantum Hall state. (2004) (369)
Topological Quantum Computation (2001) (361)
Simulation of Topological Field Theories¶by Quantum Computers (2000) (268)
On the Mobius Energy of Knots and Unknots (1994) (249)
Least area incompressible surfaces in 3-manifolds (1983) (239)
Interacting anyons in topological quantum liquids: the golden chain. (2006) (225)
Reflection positivity, rank connectivity, and homomorphism of graphs (2004) (184)
Bit Threads and Holographic Entanglement (2016) (183)
Projective Plane and Planar Quantum Codes (1998) (166)
A class of P,T-invariant topological phases of interacting electrons (2003) (158)
The Two-Eigenvalue Problem and Density¶of Jones Representation of Braid Groups (2001) (156)
P/NP, and the quantum field computer (1998) (153)
Divergence-free fields : energy and asymptotic crossing number (1991) (148)
Measurement-only topological quantum computation. (2008) (115)
Topology of 4-Manifolds (PMS-39), Volume 39 (1990) (112)
Z(2)-Systolic Freedom and Quantum Codes (2002) (100)
Faster phase estimation (2013) (98)
A Magnetic Model with a Possible Chern-Simons Phase (2001) (95)
4-Manifold topology I: Subexponential groups (1995) (91)
Towards universal topological quantum computation in the ν = 5 2 fractional quantum Hall state (2005) (80)
Strange actions of groups on spheres (1987) (74)
Quantum Computation and the Localization of Modular Functors (2000) (73)
Measurement-Only Topological Quantum Computation via Anyonic Interferometry (2008) (71)
Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (2009) (70)
A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds (1996) (69)
Strange actions of groups on spheres (1987) (68)
Quantum systems on non-k-hyperfinite complexes: a generalization of classical statistical mechanics on expander graphs (2013) (68)
CLOSED GEODESICS ON SURFACES (1982) (64)
Van Kampen’s embedding Obstruction is incomplete for $2$-Complexes in $\rz^{4}$ (1994) (60)
Quantum SU(2) faithfully detects mapping class groups modulo center (2002) (55)
Kneser-Haken finiteness for bounded 3-manifolds, locally free groups, and cyclic covers (1998) (53)
Universal Geometric Path to a Robust Majorana Magic Gate (2015) (52)
4-Manifold topology II: Dwyer's filtration and surgery kernels (1995) (52)
A surgery sequence in dimension four; the relations with knot concordance (1982) (49)
Extended hubbard model with ring exchange: a route to a non-Abelian topological phase. (2003) (48)
Line of critical points in 2+1 dimensions: quantum critical loop gases and non-Abelian gauge theory. (2004) (47)
Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions (2010) (46)
Approximate Counting and Quantum Computation (2005) (45)
Λ-splitting 4-manifolds (1977) (43)
A note on topology and magnetic energy in incompressible perfectly conducting fluids (1988) (42)
Quadruple points of 3-manifolds inS4 (1978) (36)
Nonlocality & Communication Complexity (2004) (36)
Topological quantum computing with only one mobile quasiparticle. (2005) (34)
Distortion in transformation groups (2005) (33)
A Fake S 3 × R (1979) (32)
Positivity of the universal pairing in 3 dimensions (2008) (31)
Uncountably many exotic $\mathbf{R}^4$'s in standard 4-space (1992) (31)
Universal manifold pairings and positivity (2005) (31)
A universal smoothing of four-space (1986) (31)
From String Nets to Nonabelions (2006) (31)
Möbius invariance of knot energy (1993) (30)
Quantum Max-flow/Min-cut (2015) (29)
Galois Conjugates of Topological Phases (2011) (27)
Classification of Quantum Cellular Automata (2019) (27)
Links of tori and the energy of incompressible flows (1991) (26)
Weakly-Coupled non-Abelian Anyons in Three Dimensions (2011) (26)
On the (A,B)-slice problem (1989) (24)
Selected applications of geometry to low-dimensional topology (1989) (23)
Modular transformations through sequences of topological charge projections (2016) (22)
A Blueprint for a Topologically Fault-tolerant Quantum Computer (2010) (22)
Universal gates via fusion and measurement operations on SU (2 ) 4 anyons (2015) (22)
Planes triply tangent to curves with nonvanishing torsion (1980) (21)
On the asymptotics of quantum SU(2) representations of mapping class groups (2004) (20)
A new technique for the link slice problem (1985) (20)
Combinatorial relaxation of magnetic fields (1993) (19)
A geometric reformulation of 4-dimensional surgery☆ (1986) (19)
The Group Structure of Quantum Cellular Automata (2019) (18)
A decomposition theorem forh-cobordant smooth simply-connected compact 4-manifolds (1996) (17)
Powell moves and the Goeritz group (2018) (16)
Homotopically trivial symmetries of haken manifolds are toral (1983) (15)
Are the borromean rings A-B-slice☆ (1986) (15)
Double Semions in Arbitrary Dimension (2015) (14)
Whitehead3 is a “Slice” link (1988) (14)
Geometric complexity of embeddings in ℝd (2013) (13)
Z_2-Systolic-Freedom (1999) (13)
Topological Quantum Entanglement (2014) (13)
Robust Majorana magic gates via measurements (2018) (13)
Computation in discrete-time dynamical systems (1995) (12)
Diameters of Homogeneous Spaces (2002) (12)
BETTI NUMBER ESTIMATES FOR NILPOTENT GROUPS (2001) (12)
Truncation of wavelet matrices: Edge effects and the reduction of topological control (1996) (12)
Factoring the logarithmic spiral (1988) (12)
Effective Geometry, Complexity, and Universality (2021) (11)
Limit, logic, and computation (1998) (11)
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks (2006) (11)
PERCOLATION ON THE PROJECTIVE PLANE (1997) (10)
Complexity Classes as Mathematical Axioms (2008) (10)
Poly-Locality in Quantum Computing (2000) (9)
Curvature growth of some 4-dimensional gradient Ricci soliton singularity models (2019) (9)
Uniqueness theorems for taut submanifolds. (1976) (9)
K-sat on groups and undecidability (1998) (9)
An unknotting result for complete minimal surfaces R3 (1992) (8)
Slightly singular 4-manifolds (1981) (8)
Building manifolds from quantum codes (2020) (8)
A quick proof of the 4-dimensional stable surgery theorem (1980) (8)
Link compositions and the topological slice problem (1993) (8)
Lieb-Schultz-Mattis theorem for quasitopological systems (2005) (8)
Non-Abelian topological phases in an extended Hubbard model (2003) (7)
Quantum Computing with Octonions (2018) (7)
Poincaré transversality and four-dimensional surgery (1988) (7)
Elder Siblings and the Taming of Hyperbolic 3-Manifolds (1998) (6)
ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY (2014) (6)
Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses (2005) (6)
Group Width (2010) (5)
Geometric complexity of embeddings in $${\mathbb{R}^{d}}$$Rd (2013) (5)
The universe from a single particle (2020) (5)
Covering a nontaming knot by the unlink (2007) (5)
The universe from a single particle. Part II (2021) (4)
Fusion and Measurement Operations for SU$(2)_4$ Anyons (2015) (4)
Bing Topology and Casson Handles (2013) (4)
Equivariant isotopy of unknots to round circles (1995) (4)
Controlled Mather-Thurston theorems (2020) (4)
Complexity Classes as Mathematical Axioms II (2013) (4)
Research Announcement on the “Energy” of Knots (1992) (4)
Universality of single quantum gates (2014) (3)
Width of codimension two knots (2019) (3)
A magnetic model with a possible (2003) (3)
Topological arbiters (2010) (3)
Symmetry Protected Quantum Computation (2021) (3)
Surgery on codimension 2 submanifolds (1977) (3)
Interferometric Versus Projective Measurement of Anyons (2015) (3)
On the Occasion of John Gwaltney's Retirement from University of Syracuse (1998) (2)
On the classification of taut submanifolds (1975) (2)
Non-separating immersions of spheres and Bing houses (2019) (2)
$\bold{CP^{2}}$-stable theory (1994) (2)
Automorphisms of circle bundles over surfaces (1975) (2)
A Topological Phase in a Quantum Gravity Model (2008) (2)
Twisted Interferometry (2013) (2)
EXTENSION OF INCOMPRESSIBLE SURFACES ON THE BOUNDARIES OF 3-MANIFOLDS (1997) (2)
Remarks on the solution of first degree equations in groups (1978) (2)
A remark on inherent differentiability (1988) (2)
The Geometry of the Bing Involution (2022) (1)
Scalable Designs for Topological Quantum Computation with Majorana Zero Modes: Part 2 Measurement (2017) (1)
Controlled Linear Algebra (1996) (1)
Uniqueness in Haken’s Theorem (2020) (1)
Kernel(J) warns of false vacua (2011) (1)
Cancelling 1-handles and some topological imbeddings (1979) (1)
Engel groups and universal surgery models (2017) (1)
Dehn's Lemma for Immersed Loops (2017) (1)
Three-dimensional non-Abelian anyons: Degeneracy splitting and detection by adiabatic cooling (2011) (1)
A converse to (Milnor-Kervaire theorem) $\times R$ etc. (1979) (1)
Pumping conductance, the intrinsic anomalous {H}all effect, and statistics of topological invariants (2015) (1)
Quantum Gravity via Manifold Positivity (2010) (1)
Shrinking Without Doing Much At All (2022) (1)
Amenable groups and smooth topology of 4-manifolds (2015) (1)
Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads (2013) (1)
On lower bounds for Erdős-Szekeres products (2021) (1)
An Application Layer Covert Channel: Information Hiding With Cha ng (1999) (1)
Filling links and spines in 3-manifolds (2020) (1)
Symmetry breaking to Majorana Brown-Susskind metric (2022) (1)
Topological phases: An expedition off lattice (2011) (1)
Embedding Heegaard Decompositions (2019) (1)
Scalable Designs for Topological Quantum Computation with Majorana Zero Modes: Part 1, Overview (2017) (0)
Embedding thickness below the stable range (2013) (0)
Critical Metrics and Covering Number (2022) (0)
The 2-Width of Embedded 3-Manifolds (2019) (0)
New Frontiers: Interactions between Quantum Physics and Mathematics June 20-23, 2022 (2022) (0)
Spinoza, Leibniz, Kant, and Weyl (2022) (0)
CHAPTER 9. HANDLEBODIES, NORMAL BUNDLES, AND TRANSVERSALITY (1990) (0)
CHAPTER 4. PARAMETERIZATION OF CONVERGENT TOWERS (1990) (0)
Predicting human-generated bitstreams using classical and quantum models (2020) (0)
Bing Topology & Casson Handles (2013) (0)
Double Semions in Arbitrary Dimension (2016) (0)
CHAPTER 6. EMBEDDING UP TO S-COBORDISM (1990) (0)
CHAPTER 11. SURGERY (1990) (0)
Graph parameters and reflection positivity (2004) (0)
Twisted Interferometry: the topological perspective (2016) (0)
Bit Threads and Holographic Entanglement (2016) (0)
The smallest interacting universe (2022) (0)
Quantum Computation with Topological Phases of Matter (2009) (0)
Entanglement of Sections, Examples Looking for a Theory (2023) (0)
A homotopy+ solution to the A-B slice problem (2016) (0)
The Euler number (1989) (0)
CHAPTER 12. LINKS, AND REFORMULATIONS OF THE EMBEDDING PROBLEM (1990) (0)
An Improved Long-Time Bishop-Gromov Theorem Using Shear (2023) (0)
Manifolds and smooth structures (1989) (0)
Donaldson’s theory (1989) (0)
Index of Notation (1990) (0)
The universe from a single particle (2021) (0)
Simplifying 3-manifolds in R (2016) (0)
Packing Meets Topology (2022) (0)
Emergence of Symmetry: Conformal Invariance in Scaling Limits of Random Systems (2005) (0)
Simplifying 3-manifolds in R^4 (2013) (0)
CHAPTER 8. SMOOTH STRUCTURES (1990) (0)
Approximation rigidity and $h$-principle for Bing spines (2020) (0)
The search for a large-scale, error-free quantum computer is reaching an intellectual junction at which semiconductor physics, knot theory, string the- ory, anyons, and quantum Hall effects are all coming together to produce quantum immunity. (2006) (0)
Simplifying $3$-manifolds in ${\mathbb{R}}^4$ (2015) (0)
Codimension-2 surgery (1973) (0)
2 0 O ct 2 00 6 From String Nets to Nonabelions (2008) (0)
Afterword: PC4 at Age 40 (2021) (0)
A power law for the distortion of planar sets (1987) (0)
Detecting 3d Non-Abelian Anyons via Adiabatic Cooling (2011) (0)
Publisher's Note: Modular transformations through sequences of topological charge projections [Phys. Rev. B 94, 165108 (2016)] (2017) (0)
Creating the Quantum (2009) (0)
CHAPTER 2. CAPPED GROPES (1990) (0)
Certifying a compact topological $4$-manifold (2018) (0)
Topological Poincaré conjecture in dimension 4 ( the work of (2017) (0)
Universal surgery problems with trivial Lagrangian (2019) (0)
Prospecting a Possible Quadratic Wormhole Between Quantum Mechanics and Plurality (2022) (0)
THE 4 DIMENSIONAL POINCARÉ CONJECTURE (2019) (0)
CHAPTER 3. CAPPED TOWERS (1990) (0)
Immersions of punctured 4-manifolds (2022) (0)
CHAPTER 10. CLASSIFICATIONS AND EMBEDDINGS (1990) (0)
Nonlinear Stability in Fluids and Plasma Dynamics-Conformal Quasi- Conformal Geometry: Iteration, Distoration, Dynamics and Circle Packing (1990) (0)
Enhanced Bishop-Gromov Theorem (2022) (0)
G T ] 2 4 M ay 2 00 5 Universal Manifold Pairings and Positivity (2005) (0)
1 F eb 2 01 1 Topological Phases : An Expedition o ff Lattice (2010) (0)
Non-Abelian topological phases (2006) (0)
Index of Terminology (1990) (0)
Building a Topological Quantum Computer 101 (2017) (0)
Interacting anyons in one dimension: The Fibonacci chain (2007) (0)
The topological classification of simply-connected 4-manifolds (1989) (0)
CHAPTER 5. THE EMBEDDING THEOREMS (1990) (0)
v 1 4 J an 2 00 1 Topological Quantum Computation (2002) (0)
2 9 Se p 20 04 ON THE ASYMPTOTICS OF QUANTUM SU ( 2 ) REPRESENTATIONS OF MAPPING CLASS GROUPS (2004) (0)
Classification of Quantum Cellular Automata (2020) (0)
CHAPTER 7. h-COBORDISMS (1990) (0)
Stable 1d non-Fermi liquids and lattice theory (2018) (0)
CHAPTER 1. BASIC TOOLS (1990) (0)
Quantum Loop Gas Approach to Topological States of Matter (2004) (0)
ec 2 00 2 Diameters of Homogeneous Spaces (2008) (0)

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