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Abstracts for MPIM Topology Seminar

Alternatively have a look at the program.

Slicing knots

Posted in
Speaker: 
Stefan Friedl
Affiliation: 
Regensburg
Date: 
Mon, 18/04/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

A knot in S^{4n+3} is called slice if it bounds a disk in the bounding ball D^{4n+4}.
We will discuss the obstructions to a knot K being slice. In particular we will discuss
a daring/foolish conjectural criterion for a knot in S^3 to be slice.

Stable Classification of 4-manifolds

Posted in
Speaker: 
Markus Land
Affiliation: 
U Bonn
Date: 
Mon, 25/04/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In the first part of the talk, as a warm-up, I will remind the audience of Freedmans classification
of simply connected 4-manifolds. I will then go over to the weaker classification up to stable homeomorphism
and explain how this is related to calculating bordism groups and explain the role the fundamental group plays.
In the second part I will then report on a joint paper with D. Kasprowski, M. Powell and P. Teichner about the
stable classification of 4-manifolds whose fundamental group is COAT, i.e. that of a closed orientable aspherical three-manifold.

Intermediate von Neumann signatures of knots

Posted in
Speaker: 
Peter Teichner
Affiliation: 
MPIM
Date: 
Mon, 02/05/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The Farrell-Jones conjecture for A-theory and applications

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Speaker: 
Nils Enkelmann
Affiliation: 
U Bonn
Date: 
Mon, 09/05/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Alexander-type invariants of hypersurface complements

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Speaker: 
Laurentiu Maxim
Affiliation: 
University of Wisconsin-Madison/MPIM
Date: 
Mon, 23/05/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

By analogy with knot theory, complex hypersurfaces can be studied via Alexander-type
invariants of their complements. I will discuss old and new results concerning rigidity
properties of such invariants, including twisted Alexander invariants, L^2 betti numbers
and Novikov homology of hypersurface complements.

Approximately fibering a manifold over an aspherical one

Posted in
Speaker: 
Wolfgang Steimle
Affiliation: 
Augsburg
Date: 
Mon, 30/05/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In this talk we address the problem whether a given map from some closed connected'
manifold to an aspherical closed manifold ''approximately fibers'', i.e., is homotopic to
Manifold Approximate Fibration.
We define elements in certain algebraic K-groups which are zero if the approximate fibering
problem can be solved; under certain conditions their vanishing is also a sufficient condition.
This is joint work with Tom Farrell and Wolfgang Lück.

Stable moduli spaces of odd dimensional manifolds

Posted in
Speaker: 
Fabian Hebestreit
Date: 
Mon, 13/06/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Understanding characteristic classes of manifolds bundles is one of the key topics in the
study of manifolds and their automorphisms. The advent of cobordism categories through
the work of Madsen, Tillmann and Weiss introduced a new method for studying such groups.
Its application in high dimensions was spearheaded by Galatius and Randal-Williams in the
case of highly connected even-dimensional manifolds by identifying groups of stable
characteristic classes with the cohomology of certain computationally accessible infinite

Immersed Morse theory

Posted in
Speaker: 
Mark Powell
Affiliation: 
U du Quebec, Montréal
Date: 
Mon, 20/06/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

We will consider an immersion of a manifold M into another manifold N. The k-th
stratum of N is the subset of points for which the inverse image in M consists of k
points. An immersed Morse function, roughly speaking, is a function from N to the
real numbers, that restricts to a Morse function on each stratum.
I will describe joint work with Maciej Borodzik, in which we develop this theory
analogously to classical Morse theory.
I will explain some of the applications we have gleaned thus far, as time permits.

Aspherical homology manifolds

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Speaker: 
Tibor Macko
Affiliation: 
U Bonn
Date: 
Mon, 04/07/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The Farrell-Jones conjecture implies the Borel conjecture for aspherical topological manifolds
which is a uniqueness statement: every homotopy equivalence of aspherical manifolds is
homotopic to a homeomorphism (the dimension has to be at least 5). There is also a corresponding
existence question: let G be a discrete torsion-free group such that BG has an n-dimensional model
which is a Poincare duality space. Is there a manifold model for BG? This question is currently open
even if the Farrell-Jones conjecture for G is known. The Farrell-Jones conjecture only implies the

Mapping class group, codes and generalized Kummer surfaces

Posted in
Speaker: 
Matthias Kreck
Affiliation: 
U Bonn
Date: 
Mon, 11/07/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

 In this talk codes are binary codes. They show up in topology as follows. Let M be a closed
3-manifold with involution and finite fixed point set F. Then the image in equivariant chomology
of H^1_{Z/2}(M;Z/2) \to H^1_{Z/2}(F;Z/2) = Z/2^r is a code. Poincare-Lefschetz duality implies
that this is a self dual code. These are codes with very interesting relations to positive definite
unimodular bilinear forms over Z (and so to modular forms). This relation indicates that it is

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