Seventy first meeting of the Transpennine Topology Triangle

Department of Mathematics and Computer Science
University of Leicester
Monday 7th December 2008


Coffee and tea will be available from 10.30 am.


Chris Braun (Leicester): Topological field theory and Moduli spaces of Klein surfaces

Abstract: The ribbon graph decomposition of moduli space gives orbi-cell complexes homotopy equivalent to moduli spaces of Riemann surfaces. Ribbon graphs are related to the A-infinity operad which gives a dual interpretation (due to Kevin Costello) of this in terms of topological conformal field theory. I will explain a generalisation of TFTs allowing unorientable manifolds and outline how this leads to a Möbius graph decomposition for moduli spaces of Klein surfaces (real algebraic curves). I will also mention another quite different partial compactification of these spaces, closer in spirit to the operad of Deligne-Mumford moduli spaces, with a different graph complex.

Nick Gurski (Sheffield): Categorical models for stable homotopy types

Abstract: One of the guiding principles of higher category theory is the Homotopy Hypothesis: whatever ``n-dimensional groupoids'' are, they should model homotopy n-types (spaces whose homotopy groups vanish above dimension n). This talk will be about the stable version of this hypothesis in low dimensions. In particular, I will emphasize how coherence theorems for certain categorical structures are central to the question of modeling stable homotopy types. The work in this talk is joint with Mikhail Kapranov.

Tea and Coffee will be available in F9 Mathematics Building from 11am. There will be opportunity for those interested to find a drink/meal after the last talk; arrangements made on the day The TTT is 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, (or John Hunton or Nige Ray if you are interested, so we can make approximately the right amount of tea and coffee.

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