Results on the topology of generalized real Bott manifolds

2017/10/17 by Raisa Dsouza, Dsouza, Raisa, Uma, V
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 55R99 #Secondary: 57S25 #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.1710.06093

openalex publication_date 2017/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalized Bott manifolds (over \mathbb C and \mathbb R) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We give a presentation of the fundamental group, prove that it is solvable and give a characterization for it to be abelian. We further prove that these manifolds are aspherical only in the case of real Bott manifolds and compute the higher homotopy groups. Furthermore, using the presentation of the cohomology ring with \mathbb Z₂-coefficients, we derive a combinatorial characterization for orientablity and spin structure.

Citations

• Bott towers, complete integrability, and the extended character of representations

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• Spin Structures on Generalized Real Bott Manifolds
• Some results on the topology of real Bott towers
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• Classification of real Bott manifolds and acyclic digraphs
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