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2023 | OriginalPaper | Chapter

Fundamental Groupoids and Homotopy Types of Non-compact Surfaces

Authors : Sergiy Maksymenko, Oleksii Nikitchenko

Published in: Groups, Invariants, Integrals, and Mathematical Physics

Publisher: Springer Nature Switzerland

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Abstract

The paper contains an application of van Kampen theorem for groupoids to computation of homotopy types of certain class of non-compact foliated surfaces obtained by at most countably many strips \(\mathbb {R}\times (0,1)\) with boundary intervals in \(\mathbb {R}\times \{\pm 1\}\) along some of those intervals.

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Recall that a collections of subsets {Q_i}_{i ∈ Λ} of a topological space X is called discrete, if for each i ∈ Λ there exists an open neighborhood U_i of Q_i such that \(U_i\cap U_j=\varnothing \) for i ≠ j ∈ Λ.

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Title: Fundamental Groupoids and Homotopy Types of Non-compact Surfaces
Authors: Sergiy Maksymenko
Oleksii Nikitchenko
Publisher: Springer Nature Switzerland
Book: Groups, Invariants, Integrals, and Mathematical Physics
Print ISBN: 978-3-031-25665-3

Electronic ISBN: 978-3-031-25666-0

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-3-031-25666-0_5

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