Welcome to Tim Cochran's Home Page

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

• 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!




Recent Papers:

All of the research below was partially supported by the National Science Foundation.
• The geometry of the knot concordance space , submitted, (with S. Harvey)
• Counterexamples to Kauffman's conjectures on slice knots , Advances in Math., to appear (with C. Davis)
• Structure in the bipolar filtration of topologically slice knots , Alg and Geometric Topology, to appear (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.

The papers below are already published. Published versions are the definitive versions.

• 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 L²-signatures (with Kent Orr and Peter Teichner), Annals of Math. (2), Vol. 157 (2003), no. 2, 433--519
• 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

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