Education
Later, he was an undergraduate at Massachusetts Institute of Technology, and received his Doctor of Philosophy from the University of California, Berkeley in 1982 (Embedding 4-manifolds in S5).
Later, he was an undergraduate at Massachusetts Institute of Technology, and received his Doctor of Philosophy from the University of California, Berkeley in 1982 (Embedding 4-manifolds in S5).
Tim Cochran was a valedictorian for the Severna Park High School Class of 1973. He then returned to Massachusetts Institute of Technology as a C.L.E. Moore Postdoctoral Instructor from 1982 to 1984. He was an National Science Foundation postdoctoral fellow from 1985 to 1987.
Following brief appointments at Berkeley and Northwestern University, he started at Rice University as an associate professor in 1990.
He became a full professor at Rice University in 1998. He died unexpectedly, aged 59, on December 16, 2014, while on a year-long sabbatical leave supported by a fellowship from the Simons Foundation.
With his coauthors Kent Orr and Peter Teichner, Cochran defined the solvable filtration of the knot concordance group, whose lower levels encapsulate many classical knot concordance invariants. Cochran was also responsible for naming the slam-dunk move for surgery diagrams in low-dimensional topology.
Knot Concordance, Whitney Towers and L2-signatures (with Kent Orr and Peter Teichner), Annals of Primary decomposition and the fractal nature of knot concordance (with Shelly Harvey and Constance Leidy), Counterexamples to Kauffman’s conjectures on slice knots (with Christopher Davis), Advances in, to appear.
Selected publications Four-manifolds which embed in R6 but not in R5 and Seifert manifolds for fibered knots, Inventiones Math. 77 (1984), 173–184 Geometric invariants of link cobordism, Commentarii Math. Helvetii 60 (1985), 291–311. Derivatives of links: Massey products and Milnor’s concordance invariants, Memoirs of Amer.
Math. Soc. 84 no. 427 (1990) Not all links are concordant to boundary links (with Kent Orr), Annals of Mathematics 138 (1993), 519–554. Knot Concordance, Whitney Towers and L2-signatures (with Kent Orr and Peter Teichner), Annals of Math. 157 (2003), 433–519. Structure in the Classical Knot Concordance Group (with Kent Orr and Peter Teichner), Commentarii Mathematica 79, no. 1 (2004), 105–123. Noncommutative Knot Theory, Algebraic and Geometric Topology 4 (2004), 347–398. Homology and Derived Series of Groups II: Dwyer's Theorem, (with Shelly Harvey), Geometry and Topology, 12(2008), 199-232. Knot concordance and Higher-order Blanchfield duality (with Shelly Harvey and Constance Leidy), Geometry and Topology, 13 (2009), 1419-1482. Primary decomposition and the fractal nature of knot concordance (with Shelly Harvey and Constance Leidy), Math.
Annalen, 351 no. 2, 2011, 443–508. Counterexamples to Kauffman’s conjectures on slice knots (with Christopher Davis), Advances in Math., to appear.