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July 2019 Results on the topology of generalized real Bott manifolds
Raisa Dsouza, V. Uma
Osaka J. Math. 56(3): 441-458 (July 2019).

Abstract

Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh in [4]. In this article we extend the results of [7] 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 $\mathbb Z_2$-coefficients, we derive a combinatorial characterization for orientablity and spin structure.

Citation

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Raisa Dsouza. V. Uma. "Results on the topology of generalized real Bott manifolds." Osaka J. Math. 56 (3) 441 - 458, July 2019.

Information

Published: July 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07108025
MathSciNet: MR3981299

Subjects:
Primary: 55R99
Secondary: 57S25

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 3 • July 2019
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