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Abstracts for Tree homology and Whitney towers (Semester on 4-manifolds)

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Tree homology and a conjecture of Levine

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Speaker: 
Jim Conant
Datum: 
Fre, 2013-05-17 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Tree homology and Whitney towers (Semester on 4-manifolds)

In a joint project with Rob Schneiderman and Peter Teichner, we have analyzed the structure of the set of links up to "Whitney tower concordance." A crucial aspect of this analysis is a conjecture of Jerry Levine, which relates an algebraically defined Lie ring to a combinatorially defined abelian group of labeled trees modulo the IHX relation. This conjecture is easy to verify after tensoring with a field of characteristic $0$, but the general statement is not so easy.

Geometric filtrations of string links and homology cylinders

Posted in
Speaker: 
Jim Conant
Datum: 
Die, 2013-05-21 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Tree homology and Whitney towers (Semester on 4-manifolds)

(Joint with Schneiderman and Teichner)
We analyze several filtrations on the groups of concordance classes of string links and homology
cylinders modulo homology bordism. In particular we compare the twisted Whitney tower
filtration of string links to the Johnson filtration of string links, showing that the associated
graded groups differ by finitely generated 2-torsion groups, corresponding to higher-order
Arf invariants. We also continue Jerry Levine's analysis of the Johnson filtration of homology

 

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