Journal of the Mathematical Society of Japan

A new graph invariant arises in toric topology

Suyoung CHOI and Hanchul PARK

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Abstract

In this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the $i$-th (rational) Betti number of the real toric variety associated to a graph associahedron $P_{\B(G)}$. It can be calculated by a purely combinatorial method (in terms of graphs) and is denoted by $a_i(G)$. To our surprise, for specific families of the graph $G$, our invariants are deeply related to well-known combinatorial sequences such as the Catalan numbers and Euler zigzag numbers.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 2 (2015), 699-720.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1429624600

Digital Object Identifier
doi:10.2969/jmsj/06720699

Mathematical Reviews number (MathSciNet)
MR3340192

Zentralblatt MATH identifier
1326.57044

Subjects
Primary: 55U10: Simplicial sets and complexes
Secondary: 57N65: Algebraic topology of manifolds 05C30: Enumeration in graph theory

Keywords
graph associahedron toric topology real toric variety graph invariant poset topology shellable poset

Citation

CHOI, Suyoung; PARK, Hanchul. A new graph invariant arises in toric topology. J. Math. Soc. Japan 67 (2015), no. 2, 699--720. doi:10.2969/jmsj/06720699. https://projecteuclid.org/euclid.jmsj/1429624600


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