Frank Quinn
Encyclopedia
Frank Stringfellow Quinn, III is an American
mathematician
and professor of mathematics at Virginia Polytechnic Institute and State University
, specializing in geometric topology
. He contributed to the mathematical field of 4-manifold
s, 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 R.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.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and professor of mathematics at Virginia Polytechnic Institute and State University
Virginia Polytechnic Institute and State University
Virginia Polytechnic Institute and State University, popularly known as Virginia Tech , is a public land-grant university with the main campus in Blacksburg, Virginia with other research and educational centers throughout the Commonwealth of Virginia, United States, and internationally.Founded in...
, specializing in geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
. He contributed to the mathematical field of 4-manifold
4-manifold
In mathematics, 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
Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a 'controlled' way, introduced by . Surgery refers to cutting out parts of the manifold and replacing it with a part of another manifold, matching up along...
, 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 R.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.
Selected publications
- Frank Quinn, Ends of maps. I. Ann. of Math.Annals of MathematicsThe Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
(2) 110 (1979), no. 2, 275—331. - Frank Quinn, Ends of maps. II. Invent. Math.Inventiones MathematicaeInventiones Mathematicae, often just referred to as Inventiones, is a mathematical journal published monthly by Springer Verlag. It was founded in 1966.-Editors:...
68 (1982), no. 3, 353—424. - Frank Quinn, Ends of maps. III. Dimensions 4 and 5. J. Differential Geom.Journal of Differential GeometryThe Journal of Differential Geometry is a peer-reviewed mathematical journal published by the Lehigh University. The journal publishes nine issues per year and is distributed by International Press. Surveys in Differential Geometry] It also publishes an annual supplement in book form called...
17 (1982), no. 3, 503—521. - Michael FreedmanMichael FreedmanMichael Hartley Freedman is a 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 Poincaré conjecture. Freedman and Robion Kirby showed that an exotic R4 manifold exists.Freedman was born...
and Frank Quinn, Topology of 4-manifolds. Princeton Mathematical Series, 39. Princeton University PressPrinceton University Press-Further reading:* "". Artforum International, 2005.-External links:* * * * *...
, Princeton, NJ, 1990. viii+259 pp. ISBN 0-691-08577-3 - Vyacheslav S. Krushkal and Frank Quinn, Subexponential groups in 4-manifold topology. Geom. Topol.Geometry and TopologyGeometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications...
4 (2000), 407—430.