University of Leicester

December 1st, 2003

- 11.30 Ken Edwards LT3: Jelena Grbic (Aberdeen)

``Homotopoy associative, homotopy commutative universal spaces of 2-cell complexes.'' - 12.45 Lunch
- 2.30 Bennett LT5: David Chataur (Angers)

``A bordism approach to string topology.'' - 3.45 Tea
- 4.30 Bennett LT5: David Chataur (Angers)

``The homology of free loop spaces as a homological conformal field theory.''

Title: Homotopy associative, homotopy commutative universal spaces of
2-cell complexes.

Abstract: For any connected space X the James construction shows that
$\Omega\Sigma X$ is universal in the category of homotopy associative H-spaces
in the sense that any map from X to a homotopy associative H-space Y factors
through a uniquely determined H-map $F:\Omega\Sigma X \longrightarrow Y$. In
this talk we investigate the universal spaces of two-cell complexes in the
category of homotopy associative, homotopy commutative $H$-spaces. The universal
spaces we obtain generalise a result of Cohen, Moore, and Neisendorfer
concerning odd dimensional odd-primary Moore spaces.

First Talk: A bordism approach to string topology.

Abstract: In this talk I will explain how to use geometric homology theory in
order to construct the BV-structure of Chas and Sullivan on the homology of free
loop spaces. All these constructions will use transversality in the context of
infinite dimensional manifolds.

Second Talk: The homology of free loop spaces as a homological conformal field
theory.

Abstract: One of the most exciting conjecture in String topology is the fact the
homology of free loop spaces should be a homological conformal field theory,
this algebraic structure is very rich. We will explain that a Prop, namely the
homology of the Sullivan's chord diagrams, acts on the homology of free loop
spaces. The Prop of Sullivan's chord diagrams is very close to moduli spaces of
curves and this result unifies under the same algebraic structure: The BV
structure due to Chas and Sullivan and the Frobenius structure of Cohen and
Godin.

TTT42 is partially supported by an LMS Scheme 3 grant. Please let Frank Neumann know if you will be joining us for lunch, as he needs to make specific bookings. Anyone who wishes to participate is welcome: we shall operate the usual arrangements for assistance with travel expenses.

Tea and Coffee will be served in the common room.

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

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