Thirty ninth meeting of the Transpennine Topology Triangle

Department of Mathematics and Computer Science
University of Leicester
March 4th, 2003

Programme

Coffee will be available in F9 from 11.00 am, and the first talk will start at 11.30 am.

11.30:Simona Paoli (Warwick)
(Co)homology of crossed modules)
12.45 Lunch
2.30: Javier Gutierrez (UAB Barcelona and Sheffield)
Homotopy localizations of Eilenberg--MacLane spectra
3.30 Tea
4.00:Pascal Lambrechts (Louvain-la-Neuve)
Configuration spaces from the rational homotopy viewpoint.

Abstracts

Simona Paoli (Warwick)
Title: (Co)homology of crossed modules.
Abstract: Crossed modules are algebraic models of 2-types; these objects have topological aspects as well as purely algebraic ones, and this gives rise to different (co)homology theories: the cohomology of the classifying space and the CCG cohomology, which is a type of cotriple (co)homology. After recalling the construction of these theories I shall illustrate some further developments in the (co)homology of crossed modules; these are obtained by considering more general classes of coefficients for the cotriple (co)homology and by introducing a (co)homology of cat$^n$-groups.

Javier Gutierrez (UAB Barcelona and Sheffield)
Title: Homotopy localizations of Eilenberg--MacLane spectra
Abstract: We prove that stable homotopical localizations preserve ring spectra and module spectra structures under suitable hypothesis. We use this fact to describe the main features of localization of $HR$-modules (i.e., stable $R$-GEMs), motivated by similar results in unstable homotopy. In particular, we compute the homological localizations of the Eilenberg--Mac\,Lane spectra $HG$ and describe all possible localizations of the integral Eilenberg--Mac\,Lane spectrum $H\mathbb{Z}$.

Pascal Lambrechts (Louvaine-la-Neuve)
Title: Configuration spaces from the rational homotopy viewpoint.
Abstract: I will discuss on the configuration space of $k$ points in a closed manifold $M$, denoted by $F(M,k)$. Fulton and McPherson have constructed an algebraic model for the rational homotopy type of $F(M,k)$ when $M$ is a smooth complex projective algebraic variety. In this talk we will discuss how this model can be generalized for other closed manifold, even though we cannot yet determine completely the rational homotopy type of $F(M,k)$. (This is a joint work with Don Stanley.)

TTT39 is partially supported by an LMS Scheme 3 grant. Please let John Hunton know if you will be joining us for lunch, as he needs to make specific bookings. Anyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses.
Tea and Coffee will be served in the common room.
For further information email John Hunton jrh7@mcs.le.ac.uk (or John Greenlees j.greenlees@sheffield.ac.uk or Nige Ray nige@ma.man.ac.uk) if you are interested, so we can make approximately the right amount of tea and coffee.

How to get there

It is a short walk from the rail station. See maps and how to get to Leicester University

The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society, and the Modern Homotopy Theory RTN

Escape routes