Osaka Journal of Mathematics

Moment-angle manifolds and connected sums of sphere products

Feifei Fan, Liman Chen, Jun Ma, and Xiangjun Wang

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Abstract

Corresponding to every finite simplicial complex $K$, there is a moment-angle complex $\mathcal{Z}_{K}$; if $K$ is a triangulation of a sphere, $\mathcal{Z}_{K}$ is a compact manifold. The question of whether $\mathcal{Z}_{K}$ is a connected sum of sphere products was considered in [3, Section 11]. So far, all known examples of moment-angle manifolds which are homeomorphic to connected sums of sphere products have the property that every product is of exactly two spheres. In this paper, we give a example whose cohomology ring is isomorphic to that of a connected sum of sphere products with one product of three spheres. We also give some general properties of this kind of moment-angle manifolds.

Article information

Source
Osaka J. Math., Volume 53, Number 1 (2016), 31-47.

Dates
First available in Project Euclid: 19 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1455892625

Mathematical Reviews number (MathSciNet)
MR3466825

Zentralblatt MATH identifier
1335.13018

Subjects
Primary: 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10] 14M25: Toric varieties, Newton polyhedra [See also 52B20] 55U10: Simplicial sets and complexes
Secondary: 57R18: Topology and geometry of orbifolds 57R19: Algebraic topology on manifolds

Citation

Fan, Feifei; Chen, Liman; Ma, Jun; Wang, Xiangjun. Moment-angle manifolds and connected sums of sphere products. Osaka J. Math. 53 (2016), no. 1, 31--47. https://projecteuclid.org/euclid.ojm/1455892625


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