Fifty-second 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 6 December 2005. This building is number 21 on the University Campus map, and lies within 5 minutes walk of Piccadilly railway station.
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
- 11.30 - 12.20, Room B009
Andrew Baker (Glasgow)
Gamma-Cohomology of rings of numerical polynomials and E-infinity structures on K_theory
There is an obstruction theory for E-infinity structures on commutative ring spectra which makes use of Gamma-cohomology, defined by Robinson and Whitehouse. This is a cohomology theory for commutative rings that is closely related to Andre-Quillen cohomology as well as to the obstruction theory of Goerss and Hopkins. Basic calculations of Gamma-cohomology were carried out by Richter and Robinson as well as Goerss and Hopkins. As far as topological applications go, the most interesting previous work has been for certain completed periodic spectra such as E_n. I will describe the calculations required to show that KU has a unique E-infinity structure, this involves calculating Gamma-cohomology of rings of numerical poynomials. We can also show that the E-infinity structure on ku is unique Unfortunately, for E(n) the relevant obstruction groups become highly non-trivial so this approach seems to be unlikely to succeed for higher periodic spectra.
- 12.30- 2.00
- 2.00-2.55, Room B010
Francis Clarke (Swansea)
Enumerating abelian groups
How many finite abelian groups are there? More precisely, given a finite set, how many of the binary operations on it make it into an abelian group? A recursion for this function is a key component in Cohen-Lenstra heuristics on the distribution of class groups. I shall give a bijective proof of the recursion in which the essential ingredient is a piece of labelled homological algebra.
- 3.00 - 3:45
- Tea (Room N2)
- 3.45 - 4.35, Room B010
Andrey Lazerev (Bristol)
The Quillen model of a manifold and string topology
We describe a Quillen-Lie model of the rational homotopy type of a closed manifold based on the notion of a symplectic C-infinity algebra (aka commutative A-infinity algebra). This description allows one to construct certain products on the homology of the loop space and equivariant loop space of a manifold minus a point. These products are similar to those introduced by Sullivan and Chas under the name 'string topology'.
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 Emily Bauer if you are interested in attending, so that we can cater for appropriate numbers.