Tim Cochran

Tim Cochran
Tim Cochran at Multnomah Falls in 2012
Born	(1955-04-07)April 7, 1955
Died	December 16, 2014(2014-12-16) (aged 59)
Nationality	American
Alma mater	University of California
Known for	Cochran–Orr–Teichner (solvable) filtration
Scientific career
Fields	Mathematics
Institutions	Rice University
Doctoral advisor	Robion Kirby
Doctoral students	Shelly Harvey

Thomas "Tim" Daniel Cochran (April 7, 1955 – December 16, 2014) was a professor of mathematics at Rice University specializing in topology, especially low-dimensional topology, the theory of knots and links and associated algebra.

Education and career

Tim Cochran was a valedictorian for the

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.

Awards and honors

While at Rice, he was named an Outstanding Faculty Associate (1992–93), and received the Faculty Teaching and Mentoring Award from the Rice Graduate Student Association (2014)^[4]

He was named a fellow of the American Mathematical Society^[5] in 2014, for contributions to low-dimensional topology, specifically knot and link concordance, and for mentoring numerous junior mathematicians.

Selected publications

• Cochran, T. (1984). "Four-manifolds which embed in ${\displaystyle \mathbb {R} ^{6}}$ but not in ${\displaystyle \mathbb {R} ^{5}}$ and Seifert manifolds for fibered knots". Inventiones Mathematicae. 77: 173–184.
  S2CID 121286879
  .
• Cochran, Tim D. (1985). "Geometric invariants of link cobordism". Commentarii Mathematici Helvetici. 60: 291–311.
  S2CID 120444453
  .
• Cochran, Tim D. (1990). "Derivatives of links: Massey products and Milnor's concordance invariants". Memoirs of the American Mathematical Society. 84 (427).
  doi:10.1090/memo/0427
  .
• Cochran, Tim D.; Orr, Kent E. (1993). "Not all links are concordant to boundary links". Annals of Mathematics. 138 (3): 519–554.
  JSTOR 2946555
  .
• Cochran, Tim D.; Orr, Kent E.; Teichner, Peter (2003). "Knot Concordance, Whitney Towers and ${\displaystyle L^{2}}$-signatures". Annals of Mathematics. 157 (2): 433–519.
  doi:10.4007/annals.2003.157.433
  .
• Cochran, Tim D.; Orr, Kent E.;
  doi:10.1007/s00014-001-0793-6
  .
• Cochran, Tim D. (2004). "Noncommutative Knot Theory". Algebraic and Geometric Topology. 4: 347–398.
  doi:10.2140/agt.2004.4.347
  .
• Cochran, Tim D.; Teichner, Peter (2007). "Knot Concordance and von Neumann ${\displaystyle \rho }$-invariants". Duke Mathematical Journal. 137 (2): 337–379.
  S2CID 119495376
  .
• Cochran, Tim D.;
  doi:10.2140/gt.2008.12.199
  .
• Cochran, Tim D.;
  doi:10.2140/gt.2009.13.1419
  .
• Cochran, Tim D.;
  S2CID 7556758
  .
• Cochran, Tim D.; Davis, Christopher William (2015). "Counterexamples to Kauffman's conjectures on slice knots".
  doi:10.1016/j.aim.2014.12.006
  .