## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 69, Number 2 (2017), 693-714.

### Pseudograph and its associated real toric manifold

Suyoung CHOI, Boram PARK, and Seonjeong PARK

#### Abstract

Given a simple graph $G$, the graph associahedron $P_G$ is a convex polytope whose facets correspond to the connected induced subgraphs of $G$. Graph associahedra have been studied widely and are found in a broad range of subjects. Recently, S. Choi and H. Park computed the rational Betti numbers of the real toric variety corresponding to a graph associahedron under the canonical Delzant realization. In this paper, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss and Forcey, and then discuss how to compute the Poincaré polynomial of the real toric variety corresponding to a pseudograph associahedron under the canonical Delzant realization.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 69, Number 2 (2017), 693-714.

**Dates**

First available in Project Euclid: 20 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1492653643

**Digital Object Identifier**

doi:10.2969/jmsj/06920693

**Mathematical Reviews number (MathSciNet)**

MR3638281

**Zentralblatt MATH identifier**

1376.57022

**Subjects**

Primary: 55U10: Simplicial sets and complexes

Secondary: 57N65: Algebraic topology of manifolds 05C30: Enumeration in graph theory

**Keywords**

pseudograph associahedron real toric variety

#### Citation

CHOI, Suyoung; PARK, Boram; PARK, Seonjeong. Pseudograph and its associated real toric manifold. J. Math. Soc. Japan 69 (2017), no. 2, 693--714. doi:10.2969/jmsj/06920693. https://projecteuclid.org/euclid.jmsj/1492653643