Title: Cohomology of configuration spaces of surfaces and related mapping spaces
Speaker: Craig Westerland
Speaker Info: University of Michigan
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Abstract:
Configuration spaces of points in Euclidean spaces play an important role in the operadic description of loop spaces, due to May and others. Configurations of points in the plane - part of the model for the double loops on the second suspension of a space - are used in a number of applications, from braid groups to the construction of elements of the stable homotopy groups of spheres. In this talk, we will discuss configurations on other surfaces (specifically, once-punctured closed orientable surfaces). We consider the (mod 2) cohomology of these spaces, and compute the Steenrod operations. These computations may be extended to a calculation of the Steenrod operations on the cohomology of the function space of based maps from a closed, orientable surface to an n-sphere. Some interesting modules over the Steenrod algebra result, and in certain cases we can (abstractly) realize these modules by spectra.Date: Monday, April 14, 2003