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GRAPH INVARIANTS AND BETTI NUMBERS OF REAL TORIC MANIFOLDS

Park, Boram 大阪大学 DOI:10.18910/75917

2020.04

概要

For a graph G, the graph cubeahedron □_G and the graph associahedron △_G are simple convex polytopes which admit (real) toric manifolds. In this paper, we introduce a graph invariant, called the b-number, and show that the b-numbers compute the Betti numbers of the real toric manifold X^R(□_G) corresponding to □_G. The b-number is a counterpart of the notion of anumber, introduced by S. Choi and the second named author, which computes the Betti numbers of the real toric manifold X^R(△_G) corresponding to △_G. We also study various relationships between a-numbers and b-numbers from the viewpoint of toric topology. Interestingly, for a forest G and its line graph L(G), the real toric manifolds X^R(△_G) and X^R(□_<L(G)>) have the same Betti numbers.

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