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Classifying Pl 5-Manifolds by Regular Genus: The Boundary Case

Published online by Cambridge University Press:  20 November 2018

Maria Rita Casali
Maria Rita Casali*
Affiliation:
Dipartimento di Matematica, Via Campi 213 B, I-41100 MODENA, Italy e-mail: casali@unimo.it
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Abstract

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In the present paper, we face the problem of classifying classes of orientable PL 5-manifolds M5 with h ≥ 1 boundary components, by making use of a combinatorial invariant called regular genusG(M5). In particular, a complete classification up to regular genus five is obtained: where denotes the regular genus of the boundary ∂M5 and denotes the connected sumof h ≥ 1 orientable 5-dimensional handlebodies 𝕐αi of genus αi ≥ 0 (i = 1, . . . ,h), so that .

Moreover, we give the following characterizations of orientable PL 5-manifolds M5 with boundary satisfying particular conditions related to the “gap” between G(M5) and either G(∂M5) or the rank of their fundamental group rk(π1(M5)): Further, the paper explains how the above results (together with other known properties of regular genus of PL manifolds) may lead to a combinatorial approach to 3-dimensional Poincaré Conjecture.

Keywords

57N1557Q1505C10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 193 - 211
Copyright
Copyright © Canadian Mathematical Society 1997

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