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Abstracts for Geometric Topology Seminar

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Mapping class group relations, Stein fillings, and planar open book decompositions, I

Posted in
Speaker: 
Andy Wand
Affiliation: 
MPIM
Date: 
Mon, 17/10/2011 - 16:30 - 17:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

We will discuss using mapping class group techniques to  approach
the 'geography' problem for Stein fillings of a contact  3-manifold. We
will show how these techniques give an obstruction for  a contact three
manifold to admit a planar open book decomposition,  and through examples
demonstrate independence of this obstruction from  those previously
uncovered.
 

Mapping class group relations, Stein fillings, and planar open book decompositions, II

Posted in
Speaker: 
Andy Wand
Affiliation: 
MPIM
Date: 
Mon, 17/10/2011 - 17:30 - 18:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

We will discuss using mapping class group techniques to  approach
the 'geography' problem for Stein fillings of a contact  3-manifold. We
will show how these techniques give an obstruction for  a contact three
manifold to admit a planar open book decomposition,  and through examples
demonstrate independence of this obstruction from  those previously
uncovered.
 

Results in 3-manifold topology from 2005 to 2015

Posted in
Speaker: 
Stefan Friedl
Affiliation: 
University of Cologne
Date: 
Mon, 24/10/2011 - 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

I will give a survey of some of the most important results  in 3-manifold topology since Perelman's proof of the Geometrization  Conjecture. Due to the recent results of Agol, Calegari-Gabai,  Kahn-Markovic and Wise we now have a much better understanding of  3-manifolds. Especially the new methods introduced by Wise hold the  promise to be very useful in the near future. If time permits, then I  will also talk about several applications to symplectic 4-manifolds  and minimal complexity of surfaces in 4-manifolds.
 

$L^2$-invariants and geometric group theory, I

Posted in
Speaker: 
Wolfgang Lueck
Affiliation: 
HIM
Date: 
Mon, 31/10/2011 - 16:30 - 17:15
Parent event: 
Geometric Topology Seminar

We give a short introduction to $L^2$-invariants and then
discuss their applications to geometric group theory. In the first 45
minutes we will explain and discuss recent results and in the second part we could 

$L^2$-invariants and geometric group theory II

Posted in
Speaker: 
Wolfgang Lueck
Affiliation: 
HIM
Date: 
Mon, 31/10/2011 - 17:30 - 18:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

Multisections and stable commutator lengths, I

Posted in
Speaker: 
Jonathan Bowden
Affiliation: 
MPI
Date: 
Mon, 07/11/2011 - 16:30 - 17:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

Mitsumatsu and Vogt asked whether there is a bound on the
self-intersection numbers of multisections in surface bundles over
surfaces in terms of the genus of fibre and base. We will discuss a
natural stable analogue of this question, whose solution involves the
computation of stable commutator lengths in certain stable groups and has
non-trivial implications for their original question.
 

Multisections and stable commutator lengths, II

Posted in
Speaker: 
Jonathan Bowden
Affiliation: 
MPI
Date: 
Mon, 07/11/2011 - 17:30 - 18:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

Moduli spaces of Riemann surfaces

Posted in
Speaker: 
Carl-Friedrich Bödigheimer
Affiliation: 
Bonn University
Date: 
Mon, 14/11/2011 - 16:30 - 17:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

The moduli spaces of Riemann surfaces with one (or more)  boundary curves and possible
punctures is considered. We describe  first a cell decomposition (of a compactification) and
study a  filtration of the moduli spaces. Then we define some homology  operations and present
some calculations of homology groups for genus 1, 2 and 3.
 

Moduli spaces of Riemann surfaces, II

Posted in
Speaker: 
Carl-Friedrich Bödigheimer
Affiliation: 
Bonn University
Date: 
Mon, 14/11/2011 - 17:30 - 18:15
Parent event: 
Geometric Topology Seminar

Uniform perfectness of diffeomorphism groups, I

Posted in
Speaker: 
Kojun Abe
Affiliation: 
Shinshu University
Date: 
Mon, 21/11/2011 - 16:30 - 17:15
Location: 
MPIM Lecture Hall
Parent event: 
Geometric Topology Seminar

Let D(M) be the group of diffeomorphisms of a smooth manifold M which  are isotopic to the identity through diffeomorphisms with compact  support. Herman and Thurston proved that D(M) is perfect which means  that D(M) coincides with its commutator subgroup. D(M) is said to be  uniformly perfect if each element of D(M) can be written as a product  of a bounded number of commutators. Hermann, Burago-Ivanov-Polterovich  and Tsuboi have proved that D(M) is uniformly perfect if dim(M) is not  equal to 2 or 4.

 

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