On the fundamental group of certain regular neighbourhoods. (Sobre el grupo fundamental de ciertas vecindades regulares.) (Spanish. English summary) Zbl 1321.57032

Parra, Carlos Mario; Valencia, Juan Fernando

Mat., Enseñ. Univ. (N.S.) 20, No. 2, 69-73 (2012).

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