Taras E. Panov (Moscow State University)
tpanov@higeom.math.msu.su
Goresky, Kottwitz and MacPherson introduced a combinatorial object, now called a GKM-graph, associated to a special class of symplectic manifolds with torus action. We consider a related notion of a torus graph coming from such familiar objects of "toric topology" as toric varieties, toric and torus manifolds. It appears that many results about the equivariant topology of such manifolds admit a purely combinatorial interpretations in terms of torus graphs. In particular, there is a notion of equivariant cohomology of torus graph, similar to that of a GKM-graph, and we show it to be isomorphic to the face ring of the underlying simplicial poset. We also discuss some applications to "combinatorial commutative algebra", such as detecting the class of Cohen--Macaulay simplicial posets via their face rings.
The talk is based on a joint work with Mikiya Masuda (Osaka)