Barcelona Algebraic Topology Group

The Barcelona Topology Workshop 2012 (BaToWo'12) will take place on the 30th November - 1st December. Click here for more information.

Speaker: Andrew Chermak (Kansas State University)
Title: The Normal Structure of Linking Systems
Dates: June 18th, 19th and 20th, 2012.
Hour: 12:00
Place: Room C3b-158, Facultat de Ciències, UAB.
Abstract:
We consider two problems connected with a partial normal subgroup N if a locality L.
(1) Is there a "quotient locality" L/N ?
(2) Is it possible to endow N with the structure of a locality, in such a way that that the inclusion of N in L is a homomorphism of partial groups ?
A complete answer to the first question will be provided, and a partial answer to the second.

The Barcelona Topology Workshop 2011 (BaToWo'11) will take place on the 16th December, at the Escola de Potsgrau in the UAB (how to get there). The morning lectures will take place in the room Sala de Graus, and the afternoon lectures in the room Aula 6.

Program

• 9:45 Noé Bárcenas (Universität Bonn):
  Analysis and a question on the stable homotopy type of BG.


• 11:45 Antonio Viruel (Universidad de Málaga):
  Every finite group is the group of self homotopy equivalences of an elliptic space
  
  Abstract:
  In this joint work with Cristina Costoya, we prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. Moreover, X can be chosen to be the rationalization of an inflexible compact simply connected manifold. Finally we show that faithful actions on Differential Graded Algebras do determine the isomorphism type of finite groups.
  
  
• 13:30 Lunch at Restaurant Sirius.

• 15:30 Assaf Libman (University of Aberdeen):
  A construction of free group actions on finite cell complexes equivalent to products of spheres.
  
  Abstract:
  The finite groups that can act freely on a sphere have been classified a long time ago. A classification for finite groups acting freely on a product of two spheres or more is unknown.  Assume that a finite group G acts on a finite complex which is homotopy equivalent to a product of spheres. Conjecturally the minimal possible number of spheres is the rank of G. So the problem is all about construction of such free group actions.
  In the lecture I will start with a complex representation V of a finite group G and show that it can act freely on a finite cell complex which is homotopy equivalent to a product of fix(V) spheres where fix(V) is the fixity of the representation V. The basic idea is to use the Stiefel manifolds associated with V as a "templae" for a sequence of compact spaces on which G acts, eventually freely.


• 16:45 Ramón J. Flores (Universidad Carlos III, Madrid):
  Bredon homology for groups with cyclic torsion.
  
  Abstract:
  We compute the Bredon homology groups for a class of groups with cyclic torsion that contains one-relator groups, groups with asperical presentations, surface-plus-one groups and some crystallographic groups. We also obtain some applications in the context of Baum-Connes Conjecture, generalizing to a wider context previous work of Guido Mislin. This is joint work with Yago Antolín.

Organising Committee: Natàlia Castellana and Albert Ruiz (Universitat Autònoma de Barcelona).

All lectures will be at room C3b-158

Tentative program:

Monday 21st: Warming up: Meeting and welcome!

15:00  Nitu Kitchloo, Problems on the homotopy theory of Kac-Moody groups (I)

Tuesday 22nd: Kac-Moody's day
10:15  Nitu Kitchloo, Problems on the homotopy theory of Kac-Moody groups (II)
15:00 Albert Ruiz, Cohomology of Kac-Moody groups over finite fields
Afternoon: discussion time

Wednesday 23rd:
10:15 Jérôme Scherer, Homotopy nilpotence
11:45 Tilman Bauer, Dieudonné theory for Morava K-theory
Afternoon: discussion time

Thursday 24th: p-stuff's day
11:15  Carles Broto, Algebraic structure on finite loop spaces
15:00  Natalia Castellana, Beyond the classification of p-compact groups (problems on the theory of p-compact groups)
Afternoon: discussion time

Friday 25th:
10:00 Jesper Grodal (Friday's seminar talk)

Organizer: Natàlia Castellana