Frank Stringfellow Quinn, III (born 1946) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and professor of mathematics at

Virginia Polytechnic Institute and State University Virginia Tech (formally the Virginia Polytechnic Institute and State University and informally VT, or VPI) is a public land-grant research university with its main campus in Blacksburg, Virginia. It also has educational facilities in six reg ...

, specializing in

geometric topology In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topology may be said to have originat ...

Contributions

He contributed to the mathematical field of

4-manifold In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. ...

s, including a proof of the 4-dimensional annulus theorem. In

surgery theory In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by . Milnor called this technique ''surgery'', while A ...

, 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. In addition to his work in mathematical research, he has written articles on the nature and history of mathematics and on issues of mathematical education.

Awards and honors

In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

.List of Fellows of the American Mathematical Society
retrieved 2013-05-27.

Selected publications

*Frank Quinn, ''Ends of maps. I.''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

(2) 110 (1979), no. 2, 275–331. *Frank Quinn, ''Ends of maps. II.''

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors ...

68 (1982), no. 3, 353–424. *Frank Quinn, ''Ends of maps. III.'' Dimensions 4 and 5. Journal of Differential Geometry 17 (1982), no. 3, 503–521. * Michael Freedman and Frank Quinn, ''Topology of 4-manifolds.'' Princeton Mathematical Series, 39.

Princeton University Press Princeton University Press is an independent Academic publishing, publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, ...

, Princeton, NJ, 1990. viii+259 pp. *Vyacheslav S. Krushkal and Frank Quinn, ''Subexponential groups in 4-manifold topology.''

Geometry and Topology In mathematics, geometry and topology is an umbrella term for the historically distinct disciplines of geometry and topology, as general frameworks allow both disciplines to be manipulated uniformly, most visibly in local to global theorems in R ...

4 (2000), 407–430.

References

External links

Home page

''Theoretical Mathematics''
by Arthur Jaffe and Frank Quinn
AMS K-12 education Working Group
*
Frank Quinn papers
at Microsoft Academic
Prospects in Topology (AM-138), Volume 138: Proceedings of a Conference in Honor of William Browder. (AM-138)
{{DEFAULTSORT:Quinn, Frank 20th-century American mathematicians 21st-century American mathematicians Topologists Princeton University alumni Virginia Tech faculty Fellows of the American Mathematical Society 1946 births Living people