## Journal of the Mathematical Society of Japan

### Pseudograph and its associated real toric manifold

#### 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

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

Digital Object Identifier
doi:10.2969/jmsj/06920693

#### 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

#### References

• A. Björner and M. L. Wachs, Shellable nonpure complexes and posets, I, Trans. Amer. Math. Soc., 348 (1996), 1299–1327.
• M. Carr and S. L. Devadoss, Coxeter complexes and graph-associahedra, Topology Appl., 153 (2006), 2155–2168.
• M. Carr, S. L. Devadoss and S. Forcey, Pseudograph associahedra, J. Combin. Theory Ser. A, 118 (2011), 2035–2055.
• S. Choi, S. Kaji and S. Theriault, Homotopy decomposition of a suspended real toric space, Bol. Soc. Mat. Mex., 2016, arXiv:1503.07788.
• S. Choi and H. Park, A new graph invariant arises in toric topology, J. Math. Soc. Japan, 67 (2015), 699–720.
• S. Choi and H. Park, On the cohomology and their torsion of real toric objects, to appear in Forum Math., arXiv:1311.7056.
• V. I. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk, 33 (1978), 85–134.
• J. Jurkiewicz, Chow ring of projective nonsingular torus embedding, Colloq. Math., 43 (1980), 261–270.
• A. Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN, 2009 (2009), 1026–1106.
• A. Suciu and A. Trevisan, Real toric varieties and abelian covers of generalized Davis–Januszkiewicz spaces, preprint, 2012.
• A. Trevisan, Generalized Davis–Januszkiewicz spaces and their applications in algebra and topology, Ph.D. thesis, Vrije University Amsterdam, 2012.
• A. Zelevinsky, Nested complexes and their polyhedral realizations, Pure Appl. Math. Q., 2 (2006), 655–671.