Open AccessProperly 3-realizable groups
Author(s) -
R. Ayala,
M. Cárdenas,
Francisco F. Lasheras,
A. Quintero
Publication year - 2004
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-04-07628-2
Subject(s) - algorithm , annotation , computer science , artificial intelligence , type (biology) , geology , paleontology
A finitely presented group G G is said to be properly 3 3 -realizable if there exists a compact 2 2 -polyhedron K K with π 1 ( K ) ≅ G \pi _1(K) \cong G and whose universal cover K ~ \tilde {K} has the proper homotopy type of a (p.l.) 3 3 -manifold with boundary. In this paper we show that, after taking wedge with a 2 2 -sphere, this property does not depend on the choice of the compact 2 2 -polyhedron K K with π 1 ( K ) ≅ G \pi _1(K) \cong G . We also show that (i) all 0 0 -ended and 2 2 -ended groups are properly 3 3 -realizable, and (ii) the class of properly 3 3 -realizable groups is closed under amalgamated free products (HNN-extensions) over a finite cyclic group (as a step towards proving that ∞ \infty -ended groups are properly 3 3 -realizable, assuming 1 1 -ended groups are).