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On the fundamental group of certain regular neighbourhoods. (Sobre el grupo fundamental de ciertas vecindades regulares.) (Spanish. English summary) Zbl 1321.57032
Summary: In this paper, we present a modern proof of a classical result of PL topology, which is cited widely without justification. Specifically we first prove that given a polyhedron \(P\) with a regular neighbourhood \(N\), such that the codimension of the pair \((P,N)\) is greater than or equal to 3, then it follows that \(\pi_1(N) \cong \pi_1(N \backslash P)\). As a consequence, we deduce that, under the same hypothesis, \(\pi_1(P) \cong \pi_1(\partial N)\).
MSC:
57Q40 Regular neighborhoods in PL-topology
57Q05 General topology of complexes
57M05 Fundamental group, presentations, free differential calculus
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