F. Thomas Farrell

F. Thomas Farrell (born November 14, 1941 in Ohio, United States) is an American mathematician who has made contributions in the area of topology and differential geometry. Farrell is a distinguished professor emeritus of mathematics at Binghamton University.[1] He also holds a position at the Yau Mathematical Sciences Center, Tsinghua University.

F. Thomas Farrell
F. Thomas Farrell in 2020
Born	November 14, 1941 Ohio, United States
Nationality	American
Alma mater	University of Notre Dame (B.A., 1963) Yale University (Ph.D., 1967)
Known for	Farrell-Jones Conjecture Tate-Farrell cohomology
Scientific career
Fields	Topology Differential geometry
Institutions	University of California at Berkeley Pennsylvania State University University of Michigan Columbia University Binghamton University Tsinghua University
Doctoral advisor	Wu-Chung Hsiang

Biographical data

Farrell got his bachelor's degree in 1963 from the University of Notre Dame and earned his Ph.D in Mathematics from Yale University in 1967. His Ph.D. advisor was Wu-Chung Hsiang, and his doctoral thesis title was "The Obstruction to Fibering a Manifold over a Circle".[2] He was a NSF Post-doctoral Fellow at the University of California at Berkeley from 1968 to 1969, and became an Assistant Professor there from 1969 to 1972. He then went to Pennsylvania State University, where he was promoted to professor in 1978. Later he joined the University of Michigan (1979–1985) and Columbia University (1984–1992). Since 1990 Farrell has been a faculty member at SUNY Binghamton.

In 1970, Farrell was invited to give a 50-minute address at the International Congress of Mathematicians about his thesis in Nice, France.[3][4] In 1990, for their joint work on Rigidity in Geometry and Topology, his co-author Lowell E. Jones was invited to give a 45-minute address at the International Congress of Mathematicians in Kyoto, Japan.[3][5]

Mathematical contributions

Much of Farrell's work lies around the Borel conjecture. He and his co-authors have verified the conjecture for various cases, most notably flat manifolds,[6] nonpositively curved manifolds.[7]

In his thesis, Farrell solved the problem of determining when a manifold (of dimension greater than 5) can fiber over a circle.[8]

In 1977, he introduced Tate–Farrell cohomology,[9] which is a generalization to infinite groups of the Tate cohomology theory for finite groups.

In 1993, he and his co-author Lowell E. Jones introduced the Farrell–Jones conjecture[10] and made contributions on it. The conjecture plays an important role in manifold topology.

References

1. "F. Thomas Farrell faculty profile". Department of Mathematical Sciences. Binghamton University. Retrieved January 30, 2020.
2. F. Thomas Farrell at the Mathematics Genealogy Project
3. List of ICM speakers
4. Farrell, F. Thomas (1971), "The obstruction to fibering a manifold over a circle", Actes du Congrès International des Mathématiciens, 2: 69–72
5. F. Thomas Farrell; Lowell E. Jones (1991), "Rigidity in Geometry and Topology", Proc. Of the Int. Congress of Math., 1: 653–663
6. F. Thomas Farrell; Wu-Chung Hsiang (1978), "The topological-Euclidean space form problem", Inventiones Mathematicae, 45 (2): 181–192, Bibcode:1978InMat..45..181F, doi:10.1007/bf01390272, S2CID 121990181.
7. F. Thomas Farrell; Lowell E. Jones (1993), "Topological rigidity for compact nonpositively curved manifolds", Differential Geometry: Riemannian Geometry (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., 54: 229–274.
8. Farrell, F. Thomas (1971), "The obstruction to fibering a manifold over a circle", Indiana University Mathematics Journal, 21 (4): 315–346, doi:10.1512/iumj.1972.21.21024.
9. Farrell, F. Thomas (1977), "An extension of Tate cohomology to a class of infinite groups", Journal of Pure and Applied Algebra, 10 (2): 153–161, doi:10.1016/0022-4049(77)90018-4.
10. F. Thomas Farrell; L. E. Jones (1993), "Isomorphism conjectures in algebraic K-theory", Journal of the American Mathematical Society, 6 (2): 249–297, doi:10.2307/2152801, JSTOR 2152801.