OPERATIONS ON POLYHEDRAL PRODUCTS AND A NEW TOPOLOGICAL CONSTRUCTION OF INFINITE FAMILIES OF TORIC MANIFOLDS

被引：32

作者：

Bahri, A. ^{[1
]}

Bendersky, M. ^{[2
]}

Cohen, F. R. ^{[3
]}

Gitler, S. ^{[4
]}

机构：

[1] Rider Univ, Dept Math, Lawrenceville, NJ 08648 USA

[2] CUNY, Dept Math, New York, NY 10065 USA

[3] Univ Rochester, Dept Math, Rochester, NY 14625 USA

[4] Colegio Nacl, Mexico City, DF, Mexico

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2015年 / 17卷 / 02期

关键词：

polyhedral product; moment-angle complex; moment-angle manifold; quasi-toric manifold; toric manifold; quasitoric manifold; smooth toric variety; non-singular toric variety; fan; simplicial wedge; join; COMPLEXES; POLYTOPES; QUADRICS;

D O I：

10.4310/HHA.2015.v17.n2.a8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A combinatorial construction is used to analyze the properties of polyhedral products [1] and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of infinite families of toric manifolds, associated to a given one, in a way that simplifies the combinatorial input and, consequently, the presentation of the cohomology rings. The new input is the interaction of a purely combinatorial construction with natural associated geometric constructions related to polyhedral products and toric manifolds. Applications of the methods and results developed here have appeared in [24, 25, 15, 18, 10, 23], and [19].

引用

页码：137 / 160

页数：24

共 24 条

[1] THE GEOMETRIC REALIZATION OF MONOMIAL IDEAL RINGS AND A THEOREM OF TREVISAN [J].