Momentangle complexes from simplicial posets
Abstract
We extend the construction of momentangle complexes to simplicial posets by associating a certain T^mspace Z_S to an arbitrary simplicial poset S on m vertices. Face rings Z[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and CohenMacaulay rings. Our primary motivation is to study the face rings Z[S] by topological methods. The space Z_S has many important topological properties of the original momentangle complex Z_K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z_S is isomorphic to the Toralgebra of the face ring Z[S]. This leads directly to a generalisation of Hochster's theorem, expressing the algebraic Betti numbers of the ring Z[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z_S from below by proving the toral rank conjecture for the momentangle complexes Z_S.
 Publication:

arXiv eprints
 Pub Date:
 December 2009
 DOI:
 10.48550/arXiv.0912.2219
 arXiv:
 arXiv:0912.2219
 Bibcode:
 2009arXiv0912.2219L
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Commutative Algebra
 EPrint:
 17 pages, 2 pictures