Torus graphs and simplicial posets

Details Torus graphs and simplicial posets Torus graphs and simplicial posets

2005-11-23

arxiv.org/abs/math/0511582v2

Adv. Math. 212 (2007), no. 2, 458-483

Mathematics

Algebraic Topology

26 pages, LaTeX2e; examples added, some proofs expanded

Scientific paper

For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen-Macaulay if its face ring is Cohen-Macaulay. This completes the algebraic characterisation of Cohen-Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view.

Affiliated with

Also associated with

No associations

Rating

Torus graphs and simplicial posets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Torus graphs and simplicial posets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Torus graphs and simplicial posets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-543042