Resolution of Stratifolds and Connection to Mather's Abstract Pre-Stratified Spaces

Many spaces which naturally occur in topology and algebraic geometry are not manifolds, but have a decomposition as a disjoint union of manifolds. Examples include algebraic varieties, orbit spaces of proper smooth group actions on manifolds and mappings cylinders of maps between manifolds. In 1998 M. Kreck began to develop a concept of stratified spaces so called stratifolds such that their bordism theory leads to a homology theory, which has the same coefficients as singular homology. In this thesis we focus on two subclasses of stratifolds with more geometrical structure, namely p-stratifolds and cornered p-stratifolds. First, we consider p-stratifolds as objects with singularities and try to resolve them, leaving the smooth top stratum untouched. The topological definition of the resolution is modelled on the one from algebraic geometry. In the second part of the thesis we establish the connection between abstract pre-stratified spaces in the sense of J. Mather and cornered p-stratifolds.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2003

Author dc:creator

• Grinberg, Anna

Contributors dc:contributor

• Kreck, Matthias

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/3127

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:3127