# Tim Cochran

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American mathematician

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) 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](/source/Professor) of [mathematics](/source/Mathematics) at [Rice University](/source/Rice_University) specializing in [topology](/source/Topology), especially [low-dimensional topology](/source/Low-dimensional_topology), [the theory of knots and links](/source/Knot_theory) and associated algebra.

## Education and career

Cochran in 1986

Tim Cochran was a valedictorian for the [Severna Park High School](/source/Severna_Park_High_School) Class of 1973. Later, he was an undergraduate at the [Massachusetts Institute of Technology](/source/Massachusetts_Institute_of_Technology), and received his [Ph.D.](/source/Doctor_of_Philosophy) from the [University of California, Berkeley](/source/University_of_California%2C_Berkeley) in 1982 (*Embedding 4-manifolds in S5*).[1] He then returned to MIT as a C.L.E. Moore Postdoctoral Instructor from 1982 to 1984. He was an [NSF](/source/National_Science_Foundation) postdoctoral fellow from 1985 to 1987. Following brief appointments at Berkeley and [Northwestern University](/source/Northwestern_University), he started at Rice University as an [associate professor](/source/Associate_Professor) in 1990. He became a [full professor](/source/Full_professor) at Rice University in 1998. He died unexpectedly, aged 59, on December 16, 2014,[2] while on a year-long sabbatical leave supported by a fellowship from the [Simons Foundation](/source/Simons_Foundation).[3]

## Research contributions

With his coauthors [Kent Orr](https://en.wikipedia.org/w/index.php?title=Kent_Orr&action=edit&redlink=1) and [Peter Teichner](/source/Peter_Teichner), Cochran defined the [solvable filtration](https://en.wikipedia.org/w/index.php?title=Solvable_filtration&action=edit&redlink=1) of the [knot concordance group](/source/Link_concordance), whose lower levels encapsulate many classical knot concordance invariants.

Cochran was also responsible for naming the [slam-dunk](/source/Slam-dunk) move for [surgery diagrams](/source/Dehn_surgery) 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](/source/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 R 6 {\displaystyle \mathbb {R} ^{6}} but not in R 5 {\displaystyle \mathbb {R} ^{5}} and Seifert manifolds for fibered knots". *Inventiones Mathematicae*. **77**: 173–184. [doi](/source/Doi_(identifier)):[10.1007/BF01389141](https://doi.org/10.1007%2FBF01389141). [S2CID](/source/S2CID_(identifier)) [121286879](https://api.semanticscholar.org/CorpusID:121286879).

- Cochran, Tim D. (1985). "Geometric invariants of link cobordism". *[Commentarii Mathematici Helvetici](/source/Commentarii_Mathematici_Helvetici)*. **60**: 291–311. [doi](/source/Doi_(identifier)):[10.1007/BF02567416](https://doi.org/10.1007%2FBF02567416). [S2CID](/source/S2CID_(identifier)) [120444453](https://api.semanticscholar.org/CorpusID:120444453).

- Cochran, Tim D. (1990). "Derivatives of links: Massey products and Milnor's concordance invariants". *Memoirs of the American Mathematical Society*. **84** (427). [doi](/source/Doi_(identifier)):[10.1090/memo/0427](https://doi.org/10.1090%2Fmemo%2F0427).

- Cochran, Tim D.; Orr, Kent E. (1993). ["Not all links are concordant to boundary links"](http://projecteuclid.org/euclid.bams/1183555721). *Annals of Mathematics*. **138** (3): 519–554. [doi](/source/Doi_(identifier)):[10.2307/2946555](https://doi.org/10.2307%2F2946555). [JSTOR](/source/JSTOR_(identifier)) [2946555](https://www.jstor.org/stable/2946555).

- Cochran, Tim D.; Orr, Kent E.; [Teichner, Peter](/source/Peter_Teichner) (2003). ["Knot Concordance, Whitney Towers and L 2 {\displaystyle L^{2}} -signatures"](https://doi.org/10.4007%2Fannals.2003.157.433). *Annals of Mathematics*. **157** (2): 433–519. [arXiv](/source/ArXiv_(identifier)):[math/9908117](https://arxiv.org/abs/math/9908117). [doi](/source/Doi_(identifier)):[10.4007/annals.2003.157.433](https://doi.org/10.4007%2Fannals.2003.157.433).

- Cochran, Tim D.; Orr, Kent E.; [Teichner, Peter](/source/Peter_Teichner) (2004). ["Structure in the Classical Knot Concordance Group"](https://doi.org/10.1007%2Fs00014-001-0793-6). *[Commentarii Mathematici Helvetici](/source/Commentarii_Mathematici_Helvetici)*. **79** (1): 105–123. [doi](/source/Doi_(identifier)):[10.1007/s00014-001-0793-6](https://doi.org/10.1007%2Fs00014-001-0793-6).

- Cochran, Tim D. (2004). ["Noncommutative Knot Theory"](https://doi.org/10.2140%2Fagt.2004.4.347). *Algebraic and Geometric Topology*. **4**: 347–398. [arXiv](/source/ArXiv_(identifier)):[math/0206258](https://arxiv.org/abs/math/0206258). [doi](/source/Doi_(identifier)):[10.2140/agt.2004.4.347](https://doi.org/10.2140%2Fagt.2004.4.347).

- Cochran, Tim D.; [Teichner, Peter](/source/Peter_Teichner) (2007). "Knot Concordance and von Neumann ρ {\displaystyle \rho } -invariants". *Duke Mathematical Journal*. **137** (2): 337–379. [doi](/source/Doi_(identifier)):[10.1215/S0012-7094-07-13723-2](https://doi.org/10.1215%2FS0012-7094-07-13723-2). [S2CID](/source/S2CID_(identifier)) [119495376](https://api.semanticscholar.org/CorpusID:119495376).

- Cochran, Tim D.; [Harvey, Shelly](/source/Shelly_Harvey) (2008). ["Homology and Derived Series of Groups II: Dwyer's Theorem"](https://doi.org/10.2140%2Fgt.2008.12.199). *Geometry and Topology*. **12** (1): 199–232. [arXiv](/source/ArXiv_(identifier)):[math/0609484](https://arxiv.org/abs/math/0609484). [doi](/source/Doi_(identifier)):[10.2140/gt.2008.12.199](https://doi.org/10.2140%2Fgt.2008.12.199).

- Cochran, Tim D.; [Harvey, Shelly](/source/Shelly_Harvey); Leidy, Constance (2009). ["Knot concordance and Higher-order Blanchfield duality"](https://doi.org/10.2140%2Fgt.2009.13.1419). *Geometry and Topology*. **13** (3): 1419–1482. [arXiv](/source/ArXiv_(identifier)):[0710.3082](https://arxiv.org/abs/0710.3082). [doi](/source/Doi_(identifier)):[10.2140/gt.2009.13.1419](https://doi.org/10.2140%2Fgt.2009.13.1419).

- Cochran, Tim D.; [Harvey, Shelly](/source/Shelly_Harvey); Leidy, Constance (2011). "Primary decomposition and the fractal nature of knot concordance". *Mathematische Annalen*. **351** (2): 443–508. [arXiv](/source/ArXiv_(identifier)):[0906.1373](https://arxiv.org/abs/0906.1373). [doi](/source/Doi_(identifier)):[10.1007/s00208-010-0604-5](https://doi.org/10.1007%2Fs00208-010-0604-5). [S2CID](/source/S2CID_(identifier)) [7556758](https://api.semanticscholar.org/CorpusID:7556758).

- Cochran, Tim D.; Davis, Christopher William (2015). ["Counterexamples to Kauffman's conjectures on slice knots"](https://doi.org/10.1016%2Fj.aim.2014.12.006). *[Advances in Mathematics](/source/Advances_in_Mathematics)*. **274**: 263–284. [arXiv](/source/ArXiv_(identifier)):[1303.4418](https://arxiv.org/abs/1303.4418). [doi](/source/Doi_(identifier)):[10.1016/j.aim.2014.12.006](https://doi.org/10.1016%2Fj.aim.2014.12.006).

## References

1. **[^](#cite_ref-1)** [Tim Cochran](https://mathgenealogy.org/id.php?id=18770) at the [Mathematics Genealogy Project](/source/Mathematics_Genealogy_Project)

1. **[^](#cite_ref-2)** ["Rice mourns loss of mathematician Tim Cochran"](http://news.rice.edu/2014/12/18/rice-mourns-loss-of-mathematician-tim-cochran/). Retrieved December 20, 2014.

1. **[^](#cite_ref-3)** ["2 Rice mathematicians honored"](http://news.rice.edu/2014/07/09/2-rice-mathematicians-honored/). Retrieved December 20, 2014.

1. **[^](#cite_ref-4)** ["GSA honors those who support grad students at Rice"](http://news.rice.edu/2014/05/02/gsa-honors-those-who-support-grad-students-at-rice/). Retrieved December 19, 2014.

1. **[^](#cite_ref-5)** ["List of Fellows of the American Mathematical Society"](http://www.ams.org/profession/fellows-list). Retrieved December 18, 2014.

## External links

- Tim Cochran's [home page](http://math.rice.edu/~cochran/).

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