Hypersurfaces Representing a Codimension1 Homology Class

Date:
23.01.2020

Speaker:
José Pedro Quintanilha

Time:
15:45

Abstract: Any 2dimensional homology class ϕ in a compact oriented smooth 3manifold can be represented by a (possibly disconnected) properly embedded oriented surface, and in certain situations it is useful to compare distinct (isotopy clsses of) representatives.
Specifcally, we focus on the question of whether given two such surfaces S, T (up to isotopy), it is possible to find a sequence of surfaces S = S0, S1, ..., Sk = T all representing ϕ, such that each two consecutive Si are disjoint. We will give an armative answer to this question by means of a simple proof that exploits a certain combinatorial observation. In contrast with previously known results in the same vein, our proof generalises to ambient manifolds of any dimension: fixing an (n1)dimensional homology class ϕ for a compact oriented nmanifold, one can connect any two representatives of ϕ by a sequence of homologous codimension1 submanifolds, such that each two consecutive representatives are disjoint. The contents of this talk are joint work with Gerrit Herrmann and Stefan Friedl.

Place:
2.058 (20.30)