Oberseminar Geometrie, Topologie und Analysis

H. Geiges, M. Lesch, G. Thorbergsson

Sommersemester 2005

Freitag, 10:30-12:00, Seminarraum 1

15.04.05 Thomas Püttmann (Bochum)
Wiedersehen metrics and exotic involutions of Euclidean spheres.

Abstract: Starting from a thorough study of the geometry of the Gromoll-Meyer sphere we derive explicit formulas for exotic involutions of Euclidean spheres in dimension 5,6,13, and 14 and for nonlinear cohomogeneity one actions on the Euclidean spheres in dimension 5 and 13.
22.04.05 Andrew Baker (Glasgow; z.Zt. MPIM Bonn)
Minimal atomic complexes.
(joint work with Peter May)

Abstract: Various notions of atomic and indecomposable spaces and spectra have been studied by topologists in many contexts but previously there appears to be no truly systematic theory. I will describe notions of irreducible, minimal atomic and nuclear complexes and explain how they are related. Then I will show that with these relationships understood, it is very easy to identify such complexes and give some obvious as well as some less obvious examples.
29.04.05 Ian Hambleton (McMaster University, Hamilton; z.Zt. MPIM Bonn)
Finite group actions on products of spheres.

06.05.05 Fuquan Fang (Nankai Universität, z.Zt. MPIM Bonn)
Finite isometry groups of 4-manifolds with positive curvature.

Abstract: Let M be an oriented compact positively curved 4-manifold. Let G be a finite subgroup of the isometry group of M. We prove that there is a universal constant C, such that, if the order of G is odd and larger than C, then G is either abelian of rank at most 2, or non-abelian and isomorphic to a subgroup of PU(3). In the latter case, M is homeomorphic to CP2.
27.05.05 Fakultätsöffentliche Disputation um 14 Uhr im Hörsaal VIIb, Hauptgebäude:
Klaus Niederkrüger (Köln)
Compact Lie group actions on contact manifolds.

24.06.05 Wolfgang Lück (Münster)
The Baum-Connes Conjecture, Trace Maps and Chern Characters.

Abstract: We begin with an introduction to the Baum-Connes Conjecture and its applications.

We present for equivariant topological K-homology an equivariant Chern character, which is an isomorphism and lives over the subring ΛG of the rationals which is obtained from the integers by inverting the orders of all finite subgroups of G. Modulo the Baum-Connes Conjecture this gives a complete calculation of the topological K-theory of the reduced group C*-algebra in terms of group homology.

We use it and an equivariant version of the L2-index theorem of Atiyah to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that the image of the standard trace map from the projective class group of the group C*-algebra K0(C*r(G)) to the real numbers takes values in ΛG. The original Trace Conjecture of Baum and Connes predicted that its image lies in the additive subgroup of the real numbers generated by the inverses of all the orders of the finite subgroups of G, and has been disproved by Roy in 2000.
01.07.05 David Wraith (NUI Maynooth)
New surgery techniques for positive Ricci curvature.

Abstract: We explore the question of which manifolds admit Riemannian metrics of positive Ricci curvature. In particular we focus on how surgery can help in generating new families of Ricci positive manifolds. We will display some infinite families of new examples using recent surgery techniques.
08.07.05 Rostyslav O. Hryniv (z.Zt. Bonn)
Inverse spectral problems for Sturm-Liouville operators with singular potentials
Fakultätsöffentliche Disputation um 13 Uhr im Seminarraum S69, Philosophikum:
Otto van Koert (Köln)
Open books for contact five-manifolds and applications of contact homology.

13.07.05 Fakultätsöffentliche Disputation um 12 Uhr im Seminarraum 2, Mathematisches Institut:
Christian Frey (Köln)
Nicht-lokale Randwertprobleme für elliptische Operatoren.

M. Bohn, 05/2005