Big polygon spaces

Abstract

We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big polygon spaces interesting is that they exhibit remarkable new features in equivariant cohomology: The Chang-Skjelbred sequence can be exact for them and the equivariant Poincare pairing perfect although their equivariant cohomology is never free as a module over the cohomology ring of BT. More generally, big polygon spaces show that a certain bound on the syzygy order of the equivariant cohomology of compact orientable T-manifolds obtained by Allday, Puppe and the author is sharp.

20 pages; incorrect degree shift in Proposition 5.1 corrected, some typos fixed

References in corpus (2)

• Equivariant cohomology, syzygies and orbit structure
• Equivariant Poincaré-Alexander-Lefschetz duality and the Cohen-Macaulay property

Cited by in corpus (6)

• Syzygies in equivariant cohomology for non-abelian Lie groups
• A quotient criterion for syzygies in equivariant cohomology
• Syzygies in equivariant cohomology in positive characteristic
• The syzygy order of big polygon spaces
• Mutants of compactified representations revisited
• The Chang-Skjelbred lemma and generalizations