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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 [ edit ]
Cochran in 1986
Tim Cochran was a valedictorian for the Severna Park High School Class of 1973. Later, he was an undergraduate at the Massachusetts Institute of Technology , and received his Ph.D. from the University of California, Berkeley in 1982 (Embedding 4-manifolds in S5 ).[1] NSF 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,[2] Simons Foundation .[3]
Research contributions [ edit ]
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 [ edit ]
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] contributions to low-dimensional topology, specifically knot and link concordance, and for mentoring numerous junior mathematicians .
Selected publications [ edit ]
Cochran, T. (1984). "Four-manifolds which embed in
R
6
{\displaystyle \mathbb {R} ^{6}}
R
5
{\displaystyle \mathbb {R} ^{5}}
Inventiones Mathematicae . 77 doi :10.1007/BF01389141 . S2CID 121286879 .
Cochran, Tim D. (1985). "Geometric invariants of link cobordism". Commentarii Mathematici Helvetici . 60 doi :10.1007/BF02567416 . S2CID 120444453 .
Cochran, Tim D. (1990). "Derivatives of links: Massey products and Milnor's concordance invariants". Memoirs of the American Mathematical Society . 84 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. doi :10.2307/2946555 . JSTOR 2946555 .
Cochran, Tim D.; Orr, Kent E.; Teichner, Peter (2003). "Knot Concordance, Whitney Towers and
L
2
{\displaystyle L^{2}}
. Annals of Mathematics . 157 (2 ): 433–519. arXiv :math/9908117 doi :10.4007/annals.2003.157.433
Cochran, Tim D.; Orr, Kent E.; Teichner, Peter (2004). "Structure in the Classical Knot Concordance Group" . Commentarii Mathematici Helvetici . 79 1 ): 105–123. doi :10.1007/s00014-001-0793-6
Cochran, Tim D. (2004). "Noncommutative Knot Theory" . Algebraic and Geometric Topology . 4 arXiv :math/0206258 doi :10.2140/agt.2004.4.347
Cochran, Tim D.; Teichner, Peter (2007). "Knot Concordance and von Neumann
ρ
{\displaystyle \rho }
Duke Mathematical Journal . 137 (2 ): 337–379. doi :10.1215/S0012-7094-07-13723-2 . S2CID 119495376 .
Cochran, Tim D.; Harvey, Shelly (2008). "Homology and Derived Series of Groups II: Dwyer's Theorem" . Geometry and Topology . 12 1 ): 199–232. arXiv :math/0609484 doi :10.2140/gt.2008.12.199
Cochran, Tim D.; Harvey, Shelly ; Leidy, Constance (2009). "Knot concordance and Higher-order Blanchfield duality" . Geometry and Topology . 13 3 ): 1419–1482. arXiv :0710.3082 doi :10.2140/gt.2009.13.1419
Cochran, Tim D.; Harvey, Shelly ; Leidy, Constance (2011). "Primary decomposition and the fractal nature of knot concordance". Mathematische Annalen . 351 (2 ): 443–508. arXiv :0906.1373 doi :10.1007/s00208-010-0604-5 . S2CID 7556758 .
Cochran, Tim D.; Davis, Christopher William (2015). "Counterexamples to Kauffman's conjectures on slice knots" . Advances in Mathematics 274 : 263–284. arXiv :1303.4418 doi :10.1016/j.aim.2014.12.006
References [ edit ]
^ "2 Rice mathematicians honored" . Retrieved December 20, 2014 .
^ "GSA honors those who support grad students at Rice" . Retrieved December 19, 2014 .
^ "List of Fellows of the American Mathematical Society" . Retrieved December 18, 2014 .
External links [ edit ]
International
National
Academics
Other
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=Tim_Cochran&oldid=1217696554 " C a t e g o r i e s : ● 1 9 5 5 b i r t h s ● 2 0 1 4 d e a t h s ● 2 0 t h - c e n t u r y A m e r i c a n m a t h e m a t i c i a n s ● 2 1 s t - c e n t u r y A m e r i c a n m a t h e m a t i c i a n s ● A m e r i c a n t o p o l o g i s t s ● F e l l o w s o f t h e A m e r i c a n M a t h e m a t i c a l S o c i e t y ● M a s s a c h u s e t t s I n s t i t u t e o f T e c h n o l o g y a l u m n i ● R i c e U n i v e r s i t y f a c u l t y ● U C B e r k e l e y C o l l e g e o f L e t t e r s a n d S c i e n c e a l u m n i H i d d e n c a t e g o r i e s : ● A r t i c l e s w i t h s h o r t d e s c r i p t i o n ● S h o r t d e s c r i p t i o n i s d i f f e r e n t f r o m W i k i d a t a ● A r t i c l e s w i t h h C a r d s ● A r t i c l e s w i t h I S N I i d e n t i f i e r s ● A r t i c l e s w i t h V I A F i d e n t i f i e r s ● A r t i c l e s w i t h W o r l d C a t E n t i t i e s i d e n t i f i e r s ● A r t i c l e s w i t h G N D i d e n t i f i e r s ● A r t i c l e s w i t h J 9 U i d e n t i f i e r s ● A r t i c l e s w i t h L C C N i d e n t i f i e r s ● A r t i c l e s w i t h N T A i d e n t i f i e r s ● A r t i c l e s w i t h M A T H S N i d e n t i f i e r s ● A r t i c l e s w i t h M G P i d e n t i f i e r s ● A r t i c l e s w i t h Z B M A T H i d e n t i f i e r s ● A r t i c l e s w i t h S U D O C i d e n t i f i e r s
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a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
but not in 
and Seifert manifolds for fibered knots". Inventiones Mathematicae. 77: 173–184. doi:10.1007/BF01389141. S2CID 121286879.
-signatures". Annals of Mathematics. 157 (2): 433–519. arXiv:math/9908117. doi:10.4007/annals.2003.157.433.
-invariants". Duke Mathematical Journal. 137 (2): 337–379. doi:10.1215/S0012-7094-07-13723-2. S2CID 119495376.
