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Session 31. Representation Theory, Transformation Groups, and Applications
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Big polygon spaces and syzygies in equivariant cohomology |
Matthias Franz, University of Western Ontario, Canada
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Part of the talk is based on joint work with Chris Allday and Volker Puppe
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Polygon spaces are configuration spaces of polygons with
prescribed edge lengths. We present a related family of compact
orientable manifolds, called big polygon spaces. They come with a
canonical torus action, whose fixed point set is a polygon spaces.
Big
polygon spaces are particularly interesting because they provide the
only known examples of maximal syzygies in equivariant cohomology.
We
therefore review the theory of syzygies in equivariant cohomology
and
its relation to the equivariant Poincaré pairing and the "GKM
method".
We finally discuss possible relations between the syzygy order and
the
dimension of the manifold.
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