On Graph Cohomology and Betti Numbers of Hamiltonian GKM Manifolds

Abstract

In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then use this concept and tools built along the way to study Hamiltonian GKM manifolds whose moment maps are in general position. We prove some connectivity properties of the their GKM graphs and show an upper bound of their second Betti numbers, which allows us to conclude that these manifolds, in the case of dimension 8 and 10, have non-decreasing even Betti numbers up to half dimension.

30 pages, 3 figures

References in corpus (1)

• Lower Bound For The Rank Of 2-Dimensional Generic Rigidity Matroid For Regular Graphs Of Degree Four And Five

Cited by in corpus (2)

• Lower Bound For The Rank Of 2-Dimensional Generic Rigidity Matroid For Regular Graphs Of Degree Four And Five
• Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptions