This is what happens if I drink too much coffee before class!!

Tim D. Cochran Rice Mathematics Department Rice University P.O. Box 1892 Houston, TX 77005-1892 |
Tel. (713) 348-5265 Math. Dept. (713) 348-4829 Fax. (713) 348-5231 |

Professor of Mathematics.

B.S.(1977) Massachusetts Institute of Technology; Ph.D.(1982)University of California at Berkeley.

Research Interests:

Topology, Knot Theory, Three and Four-dimensional Manifolds, Group Theory.

Teaching

- Dr. Cochran's advice on Fall 2014 classes- for young MATH majors
- Dr. Cochran's advice on Fall 2014 classes- for prospective MATH MINORS
- 2014 Office hours: none, I am on sabbatical leave until July 1, 2015
- Past Teaching
- My PhD and Masters Students

Other

Research

- List of my recent papers and preprints on arxiv.org
- List of my papers on Mathscinet
- Topology Seminar
- RTG Topology Working Seminar
- Slides of some Research Lectures
- Lecture to the Faculty of Natural Science Division of Rice University as part of the Dean's Lecture Series

- Proof that I invented Bing doubling!
**The geometry of the knot concordance space**, submitted, (with S. Harvey)**Counterexamples to Kauffman's conjectures on slice knots**, submitted, (with C. Davis)**Structure in the bipolar filtration of topologically slice knots**, to appear in Alg and Geometric Topology (with P. Horn)**Knot concordance and Blanchfield duality**, preprint (with S. Harvey and C. Leidy) Most (but not all) of the results in this paper have appeared in the two papers below: Link concordance and generalized doubling operators, and Knot concordance and higher-order Blanchfield duality.**Homology cobordism and Seifert fibered 3-manifolds**, Proc.Amer.Math.Soc., 142 (2014, 4015-4024, (with Daniel Tanner)**Positive Links**, Algebraic and Geometric Topology 14 (2014)2259-2298, (with E. Tweedy)**Injectivity of Satellite operators in knot concordance**, Journal of Topology, 2014, doi: 10.1112/jtopol/jtu003,(with Chris W. Davis and Arunima Ray)**Filtering smooth concordance classes of topologically slice knots**, Geometry and Topology,2013, 17, pp. 2103-2162 (with S. Harvey and P. Horn)**Knot concordance and homology cobordism**, Proc. Amer. Math. Soc., 141 (2013), 2193-2208 ( (with B. Franklin, M. Hedden and P. Horn)**Higher-Order Signature Cocycles for Subgroups of Mapping Class Groups and Homology Cylinders**,Int.Math.Res. Notices 2012, N0.14, pp. 3311-3373; doi: 10.1093/imrn/rnr149, (with S. Harvey and P. Horn)-
**Primary Decomposition and the Fractal Nature of Knot Concordance**, Math. Annalen,351, number 2,2011, pages 443-508, DOI: 10.1007/s00208-010-0604-5 (with S. Harvey and C. Leidy) -
**The Milnor Degree of a $3$-manifold**, Journal of Topology, (2010)3(2):405-423 doi:10.1112/jtopol/jtq011; http://jtopol.oxfordjournals.org/content/3/2/405.full.pdf+html, (with P. Melvin) -
**2-Torsion in the n-solvable filtration of the Knot Concordance Group**, Proc. of London Math. Soc.(3),(2011),102,no2,257-290 (with S. Harvey and C. Leidy) -
**Homological stability of series of groups**, Pacific Math Journal, 246, No.1 (2010) 31-47, (with S. Harvey) -
**Derivatives of Knots and Second-Order Signatures**, Alg. Geom. Topology 10 (2010), 739-787 , (with S. Harvey and C. Leidy), DOI: 10.2140/agt.2010.10.739 **New Constructions of Slice Links**Commentarii Math. Helv., 84 ,no.3,(2009),617-638, (with S. Friedl and P. Teichner)-
**Knot concordance and Higher-order Blanchfield duality**Geometry and Topology, 13 (2009),1419-1482 (with S. Harvey and C. Leidy)DOI: 10.2140/gt.2009.13.1419 -
**Link concordance and generalized doubling operators**Alg.Geom.Top., 8(2008),1593-1646(with S. Harvey and C. Leidy)DOI: 10.2140/agt.2008.8.1593 **Homology and derived p-series of groups**, Jour. London Math. Soc., 2008, doi: 10.1112/jlms/jdn046, (with S. Harvey)-
**Homology and Derived Series of Groups II: Dwyer's Theorem**, Geometry and Topology, 12(2008),199-232 (with S. Harvey) -
**Higher-Order Alexander Invariants and Filtrations of the Knot Concordance Group**, Trans.Amer.Math.Soc., 360 no.3,(2008)1407-1441. (with T. Kim) -
**Knot concordance and von Neumann ρ-invariants**Duke Math. Journal,137,no.2 (2007)337-379 (with P. Teichner) -
**Knot concordance and Blanchfield duality**Oberwolfach Reports, 3,3(2006),2154-2157(with S. Harvey and C. Leidy) -
**The Growth Rate of the First Betti Number of Abelian Covers of $3$-Manifolds**Math.Proc.Cambridge Phil.Soc.,141, no.3(2006),465-476. (with Joseph Masters) -
**Homology and Derived Series of Groups**,Geometry and Topology,v.9 (2005)2159-2191 (with S. Harvey) **Noncommutative Knot Theory**, Algebraic and Geometric Topology 4 (2004), paper no. 19, pages 347-398.-
**Structure in the Classical Knot Concordance Group**, Commentarii, 79, no.1(2004), 105--123 (pdf)(with K.Orr and P. Teichner) **Knot Concordance, Whitney Towers and L**(with Kent Orr and Peter Teichner), Annals of Math. (2), Vol. 157 (2003), no. 2, 433--519^{2}-signatures**Dehn surgery Equivalence Relations on 3-Manifolds**(with A. Gerges and K.E. Orr) Math Proc Cam Phil. Soc 131(2001), 97-127. (ps)**Quantum Cyclotomic Orders of 3-Manifolds**(with Paul Melvin)(postscript includes figures)(FINAL REVISION 6/1/99)Topology,40(2001)95-125)**Finite Type Invariants of Three Manifolds**(with P. Melvin)(final revised version 8/1/99 to appear in Inventiones) (postscript) Inventiones 140(2000)45-100**Homology Cobordism and Generalizations of Milnor's Invariants**(with K.E. Orr)(AMS-TEX): Journal Knot Theory and Ram.1999 (dvi file)**Stability of Lower Central Series of Compact 3-Manifold groups**(with K.E.Orr)(AMS tex): Topology 1998 (dvi file)**Classical Link Invariants and the Hawaiian Earrings Space**(AMS-tex): JKTR 1992 (dvi file)-
**Non-trivial Links and Plats with Trivial Gassner matrices**(AMS tex):Cambrige Phil. 1996 (dvi file) -
**Homology Boundary Links and Blanchfield Forms: Concordance Classsification and New Tangle-Theoretic Constructions**(with K.E. Orr)(AMS-tex):Topology 1994 (dvi file) -
**Not All Links are Concordant to Boundary Links**(with K.E. Orr)(dvi file for amstex): Annals 1993