ICTP Mathematics Seminar - Tuesday 7 November, at 16:00 (Jose Luis CISNEROS-MOLINA)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2017


Tuesday 7, November, at 16.00 hrs.


José Luis Cisneros-Molina (UNAM, Cuernavaca)


Title: Comparison of relative group homologies and invariants of 
hyperbolic 3-manifolds

Abstract:  Let G be a discrete group. It is well known that the homology 
groups of G have both algebraic and topological definitions. Now 
consider a subgroup H of G. In the literature there are two versions of 
relative homology groups for the pair (G,H), the theory by Adamson 
generalizes in a natural way the algebraic definition, while the theory 
by Takasu generalizes in a natural way the topological definition. In 
the first part of the talk, we present both theories, we give simple 
examples that show that these theories do not coincide in general, and 
we give a sufficient condition on the subgroup H in order that the two 
theories coincide.

In the second part of the talk, we define invariants of complete, 
orientable, non compact hyperbolic 3-manifolds of finite volume, in 
Adamson relative homology groups. We explain the relation between these 
invariants and the elements in Takasu relative homology groups given by 
Zickert, which are used to define and invariant of such hyperbolic 
3-manifolds in the extended Bloch group defined by Neumann.

VENUE:  Stasi Seminar Room (ICTP Leonardo da Vinci Building, first floor)