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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
##### Keywords:
Markov theorem; polyhedron; regular neighbourhood
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