Frank Quinn | Academic Influence

Frank Quinn 's AcademicInfluence.com Rankings

Frank Quinn

Mathematics

#1792

World Rank

#2866

Historical Rank

#730

USA Rank

Measure Theory

#2640

World Rank

#3160

Historical Rank

#758

USA Rank

mathematics Degrees

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Mathematics

Frank Quinn 's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Frank Quinn Influential?

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According to Wikipedia, Frank Stringfellow Quinn, III is an American mathematician and professor of mathematics at Virginia Polytechnic Institute and State University, specializing in geometric topology. Contributions He contributed to the mathematical field of 4-manifolds, including a proof of the 4-dimensional annulus theorem. In surgery theory, he made several important contributions: the invention of the assembly map, that enables a functorial description of surgery in the topological category, with his thesis advisor, William Browder, the development of an early surgery theory for stratified spaces, and perhaps most importantly, he pioneered the use of controlled methods in geometric topology and in algebra. Among his important applications of "control" are his aforementioned proof of the 4-dimensional annulus theorem, his development of a flexible category of stratified spaces, and, in combination with work of Robert D. Edwards, a useful characterization of high-dimensional manifolds among homology manifolds.

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Frank Quinn '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

Topology of 4-manifolds (1990) (1082)
Problems in low-dimensional topology (1997) (384)
Ends of Maps, I (1979) (262)
Chern-Simons theory with finite gauge group (1991) (256)
“Theoretical mathematics”: toward a cultural synthesis of mathematics and theoretical physics (1993) (239)
Ends of maps. III. Dimensions 4 and 5 (1982) (218)
Ends of maps, II (1982) (178)
A geometric formulation of surgery (1970) (118)
Lectures on axiomatic topological quantum field theory (1991) (114)
Topology of 4-Manifolds (PMS-39), Volume 39 (1990) (112)
Homotopically stratified sets (1988) (112)
Isotopy of 4-manifolds (1986) (95)
An obstruction to the resolution of homology manifolds. (1987) (92)
Resolutions of homology manifolds, and the topological characterization of manifolds (1983) (82)
Surgery on Poincaré and normal spaces (1972) (81)
Bordism invariants of intersections of submanifolds (1974) (72)
Subexponential groups in 4-manifold topology (2000) (50)
Group categories and their field theories (1998) (42)
Open book decompositions, and the bordism of automorphisms (1979) (40)
Algebraic K‐theory over the infinite dihedral group: a controlled topology approach (2010) (38)
Algebraic $K$-theory of poly-(finite or cyclic) groups (1985) (35)
Hausdorff Conullity of Critical Images of Fredholm Maps (1972) (35)
The stable topology of 4-manifolds (1983) (31)
Response to comments on ``Theoretical Mathematics'' (1994) (31)
CONTROLLED SURGERY WITH TRIVIAL LOCAL FUNDAMENTAL GROUPS (2001) (30)
A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today (2012) (27)
Topological transversality holds in all dimensions (1988) (26)
A role for Libraries in Electronic Publication (1995) (21)
THE TRIANGULATION OF MANIFOLDS (2013) (18)
Roadkill on the electronic highway? The threat to the mathematical literature (1995) (17)
Novikov Conjectures, Index Theorems and Rigidity: Assembly maps in bordism-type theories (1995) (16)
Hyperelementary assembly for K-theory of virtually abelian groups (2005) (14)
Semifree group actions and surgery on PL homology manifolds (1975) (14)
$B_{\left( {{\text{TOP}}_n } \right)^ \sim}$ and the surgery obstruction (1971) (14)
Ends of maps and applications (1979) (11)
ENDS OF MAPS, IV: CONTROLLED PSEUDOISOTOPY (1986) (11)
Algebraic K-theory over virtually abelian groups☆ (2012) (10)
Finite nilpotent group actions on finite complexes (1978) (9)
Lectures on controlled topology: mapping cylinder neighborhoods (2002) (8)
Problems on homology manifolds (2003) (8)
Slightly singular 4-manifolds (1981) (8)
A quick proof of the 4-dimensional stable surgery theorem (1980) (8)
Almost canonical inverse images (1974) (8)
Controlled K-theory I: Basic theory (2004) (8)
SUPPLEMENT TO 'A SCIENCE-OF-LEARNING APPROACH TO MATHEMATICS EDUCATION' (2011) (7)
Applications of Topology with Control (2010) (7)
Dual decompositions of 4-manifolds (2001) (6)
Corrigendum to Resolutions of homology manifolds, and the topological characterization of manifolds (1986) (6)
The reduction of quantum invariants of 4-thickenings (2005) (5)
Extensions of maps as fibrations and cofibrations (1975) (4)
Intrinsic Skeleta and Intersection Homology of Weakly Stratified Sets (2020) (4)
Exotic homology manifolds : Oberwolfach, 2003 (2006) (4)
Handlebodies and 2-complexes (1985) (3)
A controlled-topology proof of the product structure theorem (2006) (3)
Speculations on Gromov Convergence of Stratified Sets, and Riemannian Volume Collapse (1996) (2)
Dual decompositions of 4-manifolds II: Linear invariants (2001) (2)
Doceamus... What should students get from calculus? (And how can we provide it?) (2012) (2)
DUAL DECOMPOSITIONS OF 4-MANIFOLDS II: LINEAR LINK INVARIANTS (2001) (2)
Algebraic and geometric topology : proceedings of a conference held at Rutgers University, New Brunswick, USA, July 6-13, 1983 (1985) (2)
Contemporary Proofs for Mathematics Education (2011) (2)
Dual 2-complexes in 4-manifolds (2000) (1)
Cores of s-cobordisms of 4-manifolds (2004) (1)
Representation theory, topological field theory, and the Andrews-Curtis conjecture (1992) (1)
Algebraic and Geometric Topology (1985) (1)
Problems in 4-dimensional topology (2001) (1)
Hyperelementary induction for K-theory of virtually abelian groups (2005) (1)
Cultural adaptation in mathematics and physics (2000) (1)
Homology manifolds and 4-dimensional surgery (2005) (0)
The Triangulation of Manifolds: Topology, Gauge Theory, and History (2016) (0)
Prospects in Topology (AM-138): Proceedings of a Conference in Honor of William Browder. (AM-138) (1996) (0)
CHAPTER 3. CAPPED TOWERS (1990) (0)
Prospects in topology : proceedings of a conference in honor of William Browder (1995) (0)
A construction of set theory (2020) (0)
CHAPTER 2. CAPPED GROPES (1990) (0)
CHAPTER 10. CLASSIFICATIONS AND EMBEDDINGS (1990) (0)
CHAPTER 4. PARAMETERIZATION OF CONVERGENT TOWERS (1990) (0)
Object descriptors: usage and foundation (2022) (0)
Index of Terminology (1990) (0)
An external approach to set theory (2021) (0)
CHAPTER 5. THE EMBEDDING THEOREMS (1990) (0)
CHAPTER 7. h-COBORDISMS (1990) (0)
2 7 N ov 2 00 1 CONTROLLED SURGERY WITH TRIVIAL LOCAL FUNDAMENTAL GROUPS (0)
K-theory of Virtually Abelian Groups (2005) (0)
THE NATURE OF CONTEMPORARY CORE MATHEMATICS VERSION 0.92 MAY 2010 (2010) (0)
„Teoretická matematika‟ aneb Jak smířit matematiku s teoretickou fyzikou (1996) (0)
CHAPTER 1. BASIC TOOLS (1990) (0)
Bordism of Automorphisms of Manifolds. From the Algebraic L-Theory Point of View (1996) (0)
Mathematical descendants of William Browder (1996) (0)
CHAPTER 8. SMOOTH STRUCTURES (1990) (0)
CHAPTER 12. LINKS, AND REFORMULATIONS OF THE EMBEDDING PROBLEM (1990) (0)
CHAPTER 11. SURGERY (1990) (0)
Object descriptors and set theory (2021) (0)
Index of Notation (1990) (0)
CHAPTER 6. EMBEDDING UP TO S-COBORDISM (1990) (0)
m at h . G T ] 8 N ov 1 99 8 GROUP CATEGORIES AND THEIR FIELD THEORIES (1999) (0)
CHAPTER 9. HANDLEBODIES, NORMAL BUNDLES, AND TRANSVERSALITY (1990) (0)
Dual decompositions of 4-manifolds III: S-cobordisms (2006) (0)
Relation between quantum invariants of 3-manifolds and 2-dimensional CW-complexes (2000) (0)

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