University of Sheffield

Wednesday

04/06/08

This will be a working meeting. There will therefore be the usual time for
participant discussion.

- 11.00 am: Coffee in I15

- 11.30 am, Northcott Room J11: Ieke Moerdijk (Sheffield and Utrecht)

"An extension of the notion of Reedy category"

- 2.30 pm, Northcott Room J11: Richard Garner (Uppsala and Cambridge)

"Universal cofibrant replacements" - 3.30 pm, I15: Tea
- 4.15 pm, Northcott Room J11: Ran Levi (Aberdeen)

"Some observations on a conjecture of Friedlander and Milnor."

I will present an extension of the notion of "Reedy category" having possibly
nontrivial automorphism groups. Like the classical notion, this extension has the
property that diagrams indexed by a "generalized Reedy category" still carry a
closed model structure. Unlike the classical notion, the new notion includes important
examples like Segal's category Gamma, Connes's category Lambda, and the indexing
category Omega for dendroidal sets. (Joint work with Clemens Berger.)

Richard Garner "Universal cofibrant replacements"

The work of Jeff Smith makes it relatively straightforward to construct model structures on categories of algebraic entities. It is considerably less straightforward to get out of these model structures things that you can compute with. However, this need not be so. We explain how any cofibrantly generated model structure gives rise to a canonically and universally determined notion of cofibrant replacement, and by looking at some examples, see that this frequently gives us something both tractable and useful.

Ran Levi "Some observations on a conjecture of Friedlander and Milnor."

Let $G$ be a Lie group with finitely many components, and let $G^\delta$ be the group $G$ considered as a discrete group. Friedlander and Milnor conjectured that the obvious map $BG^\delta\to BG$ induces an isomorphism on homology with any finite coefficients. Milnor showed that the conjecture holds whenever the identity component of $G$ is solvable, and that the map above induces a split epimorphism on homology with any finite coefficients. Friedlander and Mislin generalized the Isomorphism Conjecture, and showed that it is equivalent to another conjecture they named the Finite Subgroup Conjecture. In this lecture we utilize homology decomposition techniques to show that Milnor's homological splitting result follows in fact from a topological splitting, which holds after $p$-completion at any prime $p$. We use this result to obtain an easy proof of the equivalence of the Isomorphism Conjecture and the Finite Subgroup Conjecture.

Anyone who wishes to participate is welcome: we shall operate the usual
arrangements for assistance with travel expenses. We expect to assemble for tea
and coffee in I15, Floor 5, from 11.00 am until the first talk. Each lecture
will take place in Room J11 of the Hicks Building, Hounsfield Road,
Sheffield.

Tea and Coffee will be served in the common room I15.

For
further information email John Greenlees j.greenlees@sheffield.ac.uk, (or
John Hunton jrh7@mcs.le.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.

The meeting is partially supported by a Scheme 3 grant from the London Mathematical Society.

TTT meetings are partially supported by an LMS Scheme 3 grant. Anyone who
wishes to participate is welcome: we shall operate the usual arrangements for
assistance with travel expenses.

For further information email John Greenlees j.greenlees(\a\t) sheffield.ac.uk, John Hunton jrh7(\a\t) mcs.le.ac.uk or Nige Ray nige(\a\t) ma.man.ac.uk if you are interested.

To TTT64

To TTT66