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October 2022 The $\mathbb Z_2$-Betti numbers of oriented Grassmannians
Tetsuya Ozawa
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Osaka J. Math. 59(4): 843-851 (October 2022).

Abstract

The purpose of this article is to show a simple method of finding $\mathbb Z_2$-Betti numbers of oriented Grassmannians. The actual calculation is performed by computing $\mathbb Z_2$-ranks of matrices defined in a combinatorial way. For the reduction of problem from topology to matrix rank, we will analyse Morse homology of certain functions on the oriented Grassmannians.

Acknowledgments

The author would like to thank Professor Toshiaki Maeno for valuable comments.

Citation

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Tetsuya Ozawa. "The $\mathbb Z_2$-Betti numbers of oriented Grassmannians." Osaka J. Math. 59 (4) 843 - 851, October 2022.

Information

Received: 16 December 2020; Revised: 3 August 2021; Published: October 2022
First available in Project Euclid: 4 October 2022

Subjects:
Primary: 57T15
Secondary: 06A07 , 57R70

Rights: Copyright © 2022 Osaka University and Osaka Metropolitan University, Departments of Mathematics

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Vol.59 • No. 4 • October 2022
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