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Abstracts for Low dimensional topology seminar

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Whitney towers and Milnor invariants, a survey of some recent results

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Speaker: 
Peter Teichner
Affiliation: 
MPIM
Date: 
Mon, 2010-10-04 18:00 - 19:00
Location: 
MPIM Lecture Hall

Quilted Floer homology of 3-manifolds

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Speaker: 
Yanki Lekili
Affiliation: 
U of Cambridge/MPI
Date: 
Mon, 2010-10-11 18:00 - 19:00
Location: 
MPIM Lecture Hall

We introduce quilted Floer homology (QFH), a new invariant of 3-manifolds equipped with an indefinite circle valued Morse function (i.e. broken fibration). This is yet another localization of Seiberg-Witten theory and a natural extension of Perutz's 4-manifold invariants associated with broken Lefschetz fibrations, making it a (3+1) theory. We relate Perutz's theory to Heegaard Floer theory by giving an isomorphism between QFH and HF+ for extremal spin^c structures with respect to the fibre of the Morse function.

A different view on Casson-Gordon invariants for knots

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Speaker: 
Mark Powell
Date: 
Mon, 2010-10-18 18:00 - 19:00
Location: 
MPIM Lecture Hall

Contact structures on product manifolds

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Speaker: 
Hansjörg Geiges
Affiliation: 
U Köln
Date: 
Mon, 2010-10-25 18:00 - 19:00
Location: 
MPIM Lecture Hall

Contact structures, by virtue of their nonintegrability, are better adapted to twisted products (fibre bundles) than cartesian products. In this talk I shall discuss a construction of contact structures on products of $S^1$ with manifolds admitting a suitable decomposition into exact symplectic pieces. Such a decomposition will be shown to exist for symplectic 4-manifolds. This is joint work with A. Stipsicz.

An application of discrete Morse theory

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Speaker: 
Jim Conant
Affiliation: 
Univ. of Tennessee, Knoxville
Date: 
Mon, 2010-12-13 18:00 - 19:00
Location: 
MPIM Lecture Hall

Splice diagrams and universal abelian covers

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Speaker: 
Helge Møller Pedersen
Affiliation: 
Heidelberg
Date: 
Mon, 2011-01-17 16:30 - 18:00
Location: 
MPIM Lecture Hall

Decompositions of low-dimensional objects

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Speaker: 
Sergey Matveev
Affiliation: 
CSU/MPI
Date: 
Mon, 2011-01-24 16:30 - 18:00
Location: 
MPIM Lecture Hall

We develop a new version of the famous Diamond Lemma of M. H. A. Newman (1942) and use it to describe several results on decompositions of different geometric objects. 1. A spherical splitting theorem for knotted graphs in 3-manifolds. 2. Counterexamples to the folklore prime decomposition theorem for 3-orbifolds. 3. A theorem on annular splittings of 3-manifolds, which is independent of the JSJ-decomposition theorem. 4. Prime decomposition theorem for homologically trivial knots in thick surfaces.
 

Volume of Representations: Definition and Applications

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Speaker: 
Stephan Tillmann
Date: 
Mon, 2011-01-31 16:30 - 17:30
Location: 
MPIM Lecture Hall

Topological Classification of Bott manifolds

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Speaker: 
Suyoung Choi
Organiser(s): 
(Prof. Kreck, Prof. Teichner)
Affiliation: 
Ajou U, Korea
Date: 
Mon, 2011-07-11 16:30 - 17:30
Location: 
MPIM Lecture Hall

The symplectic representation of the mapping class group is unique

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Speaker: 
Mustafa Korkmaz
Affiliation: 
Middle East Technical University / MPIM
Date: 
Mon, 2011-07-25 16:30 - 17:30
Location: 
MPIM Lecture Hall

The mapping class group, MCG, of a closed orientable surface  of
genus g has classical symplectic representation coming from its  action on
the first
homology of the surface. I will show that any 2g-dimensional  nontrivial
representation of the group MCG is conjugate to this  classical
representation. I will also prove that MCG has no faithful  linear
representation in dimensions less than 3g-2. This contributes  to the
well-known problem on the linearity of MCG. Some algebraic  corollaries on

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