Doctor of Philosophy
For a compact smooth manifold with a torus action, its equivariant cohomology is a finitely generated module over a polynomial ring encoding information about the space and the action. For such a module, we can associate a purely algebraic notion called syzygy order. Syzygy order of equivariant cohomology is closely related to the exactness of Atiyah-Bredon sequence in equivariant cohomology. In this thesis we study a family of compact orientable manifolds with torus actions called big polygon spaces. We compute the syzygy orders of their equivariant cohomologies. The main tool used is a quotient criterion for syzygies in equivariant cohomology. We also generalize a lacunary principle for Morse-Bott functions to manifolds with corners in the process of computation. Some applications of the main result are discussed in the end.
Huang, Jianing, "Syzygy Order of Big Polygon Spaces" (2018). Electronic Thesis and Dissertation Repository. 5643.