# TTT68: Manchester

School of Mathematics, Alan Turing Building, University of Manchester.

## Date

19 January 2009

## Speakers

### Tony Bahri (Rider University, NJ USA)

Piecewise polynomials and the equivariant cohomology of toric varieties

Piecewise polynomials and the equivariant cohomology of toric varieties

Toric varieties have a natural torus action. For smooth varieties, the integral equivariant cohomology with respect to this action is the Stanley-Reisner ring of the underlying fan. A description of this ring in terms of piecewise polynomials on the fan allows a generalisation to a class of singular varieties which include weighted projective spaces.

Unlike ordinary cohomology, the integral equivariant cohomology distinguishes among weighted projective spaces. A report on joint work with Matthias Franz and Nigel Ray.

### Al Kasprzyk (Kent)

Simplices in toric geometry: Fake weighted projective space

Simplices in toric geometry: Fake weighted projective space

When considering toric Fano varieties, it is natural to think about simplices. In this talk I'll concentrate on one-point lattice simplicies and their associated varieties: fake weighted projective space. I hope to illustrate the difference between fake and genuine weighted projective space, and give several example calculations.

### Jon Woolf (Liverpool)

What are the homotopy groups of a stratified space?

What are the homotopy groups of a stratified space?

The usual definition of homotopy groups makes perfect sense when the space is stratified, but are there subtler invariants which capture some of the extra information in the stratification?

This talk will introduce two proposals (due respectively to MacPherson and Baez) for modifying the definition of the homotopy groups of a stratified space, illustrated by some simple examples. For MacPherson's proposal I will discuss the analogue(s) of the fact that the fundamental group classifies covering spaces and for Baez's I will discuss a conjectural relation to bordism theory.

## Further information

The meeting was jointly supported by the London Mathematical Society and MIMS.