Speaker:

Janusz Przewocki

Thursday, July 25, 2013 - from 17:30
to 17:55

Abstract:

Milnor-Thurston homology theory is a construction similar to singular homology. The first mention of this theory
can be found in Thurston's lecture notes "Geometry and topology of 3-manifolds", where it was used, for example, to prove
that the volume of a hyperbolic manifold is a topological invariant.
Zastrow and Hansen independently proved that this homology theory coincides with singular homology for
CW-complexes. However, its behaviour for spaces with a more complicated local structure is still unknown.
In this talk, we will provide some results in this direction. Milnor-Thurston homology
for the Warsaw Circle shall be calculated. Moreover, we will show that its zeroth homology is non-Hausdorff in the weak topology
considered by Berlanga.
Further, the above results lead us to some natural questions concerning Milnor-Thurston homology. Namely,
is the natural homomorphism between singular homology and Milnor-Thyrston homology always an injection?
Are there any conditions under which zeroth Milnor-Thurston homology group coincides with singular homology group?