F. Thomas Farrell

F. Thomas Farrell, 2020

Francis Thomas Farrell (born November 14, 1941 in Cincinnati , Ohio ) is an American mathematician who studies topology and differential geometry.

Life

Farrell studied at Harvard University with a bachelor's degree in 1964 and received his doctorate in 1967 with Wu-Chung Hsiang at Yale University (The obstruction to fibering a manifold over a circle). As a post-doctoral student he was at the University of California, Berkeley , where he was assistant professor from 1969 to 1972. He then went to Pennsylvania State University , where he received a full professorship in 1978. In 1976/77 he was at the Institute for Advanced Study . From 1979 to 1985 he was at the University of Michigan and from 1984 to 1992 at Columbia University . He has been a professor at the State University of New York at Binghamton since 1990.

plant

In his dissertation he proved when manifolds with dimensions greater than or equal to five fiber spaces are above the circle.

He dealt with the classification of manifolds with the same homotopy type and specifically with the Borel conjecture, which states that aspheric closed manifolds are determined by their fundamental group up to homeomorphism . The conjecture makes a topological rigidity statement (determination of the topology from algebraic data of the homotopy groups) and Farrell and colleagues proved the conjecture for special cases (some flat manifolds and those with non-positive sectional curvature in 5 and more dimensions with LE Jones). He worked in this and other areas besides Hsiang (with whom he proved special cases of the Novikov conjecture) often with Lowell Edwin Jones . The Farrell-Jones conjectures (1993) in the algebraic K-theory originate from both, the proof of which leads to other conjectures such as the Borel and Novikov conjectures (in dimensions greater than or equal to five). It is related to the Baum-Connes conjecture in the topological K-theory. Farrell's extension of Tate cohomology groups of finite groups (after John T. Tate ) is called Tate-Farrell cohomology. ${\ displaystyle \ pi _ {1} (X)}$

In 1970 he was invited to speak at the International Congress of Mathematicians in Nice ( The obstruction of fibering a manifold over a circle ) and Lowell Edwin Jones gave a lecture on the joint work at the ICM in 1990 in Kyoto (Rigidity in Geometry and Topology).

Fonts

The obstruction to fibering a manifold over a circle. In: Indiana University Mathematics Journal. Volume 21, No. 4, 1971, pp. 315-346, ( digitized version ).

An extension of Tate cohomology to a class of infinite groups. In: Journal of Pure and Applied Algebra. Volume 10, No. 2, 1977, pp. 153-161, doi : 10.1016 / 0022-4049 (77) 90018-4 .

with LE Jones: Anosov diffeomorphisms constructed from Diff . ${\ displaystyle \ pi _ {1}}$ ${\ displaystyle (S ^ {n})}$ In: Topology. Volume 17, No. 3, 1978, pp. 273-282, doi : 10.1016 / 0040-9383 (78) 90031-9 .

with W.-C. Hsiang: The topological-Euclidean space form problem. In: Inventiones Mathematicae . Volume 45, No. 2, 1978, pp. 181-192 .

with W.-C. Hsiang: On Novikov's Conjecture for Non-Positively Curved Manifolds, I. In: Annals of Mathematics . Series 2, Vol. 113, No. 1, 1981, pp. 199-209, doi : 10.2307 / 1971138 .

with W.-C. Hsiang: The stable topological-hyperbolic space form problem for complete manifolds of finite volume. In: Inventiones Mathematicae. Volume 69, No. 1, 1982, pp. 155-170 .

with LE Jones: -theory and dynamics. I. In: Annals of Mathematics. Series 2, Vol. 124, No. 3, 1986, pp. 531-569, doi : 10.2307 / 2007092 . ${\ displaystyle K}$

with LE Jones: The surgery groups of poly (finite or cyclic) groups. ${\ displaystyle L}$ In: Inventiones Mathematicae. Volume 91, No. 3, 1988, pp. 559-586 .

with LE Jones: A topological analogue of Mostow's rigidity theorem. In: Journal of the American Mathematical Society . Volume 2, No. 2, 1989, pp. 257-370, doi : 10.2307 / 1990978 .

with LE Jones: Classical aspherical manifolds. Expository lectures from the CBMS Regional Conference held at the University of Florida, January 9-14, 1989 (= Regional Conference Series in Mathematics. 75). American Mathematical Society, Providence RI 1990, ISBN 0-8218-0726-9 .

with LE Jones: Isomorphism Conjectures in Algebraic Theory. ${\ displaystyle K}$ In: Journal of the American Mathematical Society. Volume 6, No. 2, 1993, pp. 249-297, doi : 10.2307 / 2152801 .

with LE Jones: Topological rigidity for compact nonpositively curved manifolds. In: Robert Greene, Shing-Tung Yau (Ed.): Differential geometry. Volume 3: Riemannian geometry. (Proceedings of the Summer Research Institute on Differential Geometry held at the University of California, Los Angeles, Los Angeles, California July 8-28, 1990) (= Proceedings of Symposia in Pure Mathematics. 54, 3). American Mathematical Society, Providence RI 1993, ISBN 0-8218-1496-6 , pp. 229-274.

with LE Jones: Complex hyperbolic manifolds and exotic smooth structures. In: Inventiones Mathematicae. Volume 117, 1994, pp. 57-74 .

with LE Jones: Rigidity for aspherical manifolds with . ${\ displaystyle \ pi _ {1} \ subset GL_ {m} (\ mathbb {R})}$ In: The Asian Journal of Mathematics. Volume 2, No. 2, 1998, pp. 215-262, doi : 10.4310 / AJM.1998.v2.n2.a1 .

The Borel Conjecture. In: F. Thomas Farrell, Lothar Göttsche , Wolfgang Lück (Eds.): Topology of high-dimensional Manifolds. (Proceedings of the School on high-dimensional Manifold Topology, Abdus Salam ICTP, Trieste, Italy, May 21-June 8, 2001) (= ICTP Lecture Notes. 9, 1). Volume 1. ICTP - The Abdus Salam International Center for Theoretical Physics, Triest 2002, ISBN 92-95003-12-8 , pp. 227-298, ( digitized version ).

with Peter A. Linnell: -theory of solvable groups. In: Proceedings of the London Mathematical Society . Volume 87, No. 2, 2003, pp. 309-336, doi : 10.1112 / S0024611503014072 . ${\ displaystyle K}$

with Peter A. Linnell: Whitehead groups and the Bass conjecture. In: Mathematical Annals . Volume 326, No. 4, 2003, pp. 723-757, doi : 10.1007 / s00208-003-0424-y .

literature

James F. Davis: The work of Tom Farrell and Lowell Jones in topology and geometry. In: Pure and Applied Mathematics Quarterly. Volume 8, No. 1 (Special issue in honor of F. Thomas Farrell and Lowell E. Jones), 2012, pp. 1-14, doi : 10.4310 / PAMQ.2012.v8.n1.a3 .

Web links

Homepage Binghamton University

Individual evidence

↑ F. Thomas Farrell in the Mathematics Genealogy Project (English)
↑ That means the homotopy groups vanish for n> 1 ${\ displaystyle \ pi _ {n} (X)}$
↑ A topological statement of rigidity for spheres is the Poincare conjecture
^ Lück, The Farrell-Jones Conjecture and its applications, Oxford 2007, pdf

personal data
SURNAME	Farrell, F. Thomas
ALTERNATIVE NAMES	Farrell, Francis Thomas (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	November 14, 1941
PLACE OF BIRTH	Cincinnati , Ohio

[1] F. Thomas Farrell in the Mathematics Genealogy Project (English)

[2] That means the homotopy groups vanish for n> 1 ${\ displaystyle \ pi _ {n} (X)}$

[3] A topological statement of rigidity for spheres is the Poincare conjecture

[4] Lück, The Farrell-Jones Conjecture and its applications, Oxford 2007, pdf