Cubes and Generalized Real Bott Manifolds

2011/01/24 by Yu Li, Li Yu, Yu, Li
Mathematics · #05B99 #57N16 #57S17 #57S25 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AT #math.CO #math.GT #msc:05B99 #msc:57N16 #msc:57S17 #msc:57S25

paper · pdf · doi:10.48550/arxiv.1101.4452

Some small changes were made to the previous version. The introduction part was expanded and a new reference was added

openalex publication_date 2011/01/24 · arxiv created 2011/01/27 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a notion of facets-pairing structure and its seal space on a nice manifold with corners. We will study facets-pairing structures on any cube in detail and investigate when the seal space of a facets-pairing structure on a cube is a closed manifold. In particular, for any binary square matrix A with zero diagonal in dimension n, there is a canonical facets-pairing structure F_A on the n-dimensional cube. We will show that all the closed manifolds that we can obtain from the seal spaces of such F_A's are neither more nor less than all the generalized real Bott manifolds --- a special class of real toric manifolds introduced by Choi, Masuda and Suh.

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