Fifty-ninth Meeting of the Transpennine Topology Triangle

Date and Location

The talks will take place in the Mathematics and Social Science (MSS) Building, School of Mathematics, The University of Manchester on Tuesday 13 February 2007. This building is number 21 on the University Campus map, and lies within 5 minutes walk of Piccadilly railway station.

Programme

Participants will meet for coffee from 1100AM onwards in the Staff Common Room N2. Lunch will be taken in any of several local venues (such as the vegetarian "On the Eight Day", for example), and we expect to visit a nearby restaurant for early-evening dinner.

11.00 -11.30, Room N2

Coffee

11.30 - 12.20, Room B009

Andrew Baker (Glasgow)
Andre-Quillen homology as a cellular theory
Abstract: (Based on the joint work with Gilmour and Reinhard) Andre-Quillen homology (for simplicial rings) and the analogue for commutative S-algebras known as topological Andre-Quillen homology can be calculated for cellular S-algebras in terms of the cell structures. I will explain how this works and then mention applications to the study of minimal atomic p-local commutative S-algebras and simplicial commutative algebras over a Noetherian local ring, generalising analogous results of Baker, May, Pereira for p-local spaces and spectra and Alshumrani for chain complexes over a Noetherian local ring.

12.30- 2.00

Lunch

2.00-2.55, Room B009

Taras Panov (Moscow)
Algebraic torus actions, Kempf-Ness sets and real quadrics C^m
Abstract: In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical quotient with respect to a maximal compact subgroup. We show that an appropriate notion of Kempf-Ness set exists for a class of algebrai torus actions on quasiaffine varieties (coordinate subspace arrangement complements) arising in the 'geometric invariant theory' approach to toric varieties. These'toric' Kempf-Ness sets are shown to toric topologists as moment-angle complexes. In the case of a projective toric variety, the Kempf-Ness set is the level surface for the appropriate moment map and can be written as a complete intersection of real quadrics in C^m. We proceed by studying the cohomology of these Kempf-Ness sets.

3.00 - 3:45

Tea (Room N2)

3.45 - 4.35, Room B009

Victor Buchstaber (Manchester and Moscow)
The universal equivariant genus for the torus actions
Abstract: (bases on recent work with Panov and Ray) We consider the universal equivariant genus for stably complex 2n-dimensional manifolds equipped with an action of a k-dimensional torus, where K is less than or equal to n. In the case of quasitoric manifolds M we explicitly calculate this genus in terms of certain underlying combinatorial data. By way of application, we obtain a formula evaluating the complex cobordism class of M in terms of this data.

Travel support

Everyone who wishes to participate is welcome, particularly postgraduate students. We shall operate the usual criteria for assistance with travel expenses, but beneficiaries will need to complete the new Manchester University Pr7 form, described at http://www.campus.manchester.ac.uk/staffnet/policies/expensesguidelines/. Those who qualify should therefore come armed with their NI numbers, and details of their UK bank accounts. Please email MIMS secretary Sebastian Rees if you are interested in attending, so that we can cater for appropriate numbers.

Sponsors

The meeting is supported by the London Mathematical Society and MIMS

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