An algorithmic approach to construct crystallizations of 3-manifolds from presentations of fundamental groups

Basak, Biplab (2016) An algorithmic approach to construct crystallizations of 3-manifolds from presentations of fundamental groups. In: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 126 (4). pp. 629-653.

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Abstract

We have defined the weight of the pair (aOE (c) Sa R pound >,R) for a given presentation aOE (c) Sa R pound > of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two generators and two relations. If the weight of (aOE (c) Sa R pound >,R) is n, then our algorithm constructs all the n-vertex crystallizations which yield (aOE (c) Sa R pound >,R). As an application, we have constructed some new crystallizations of 3-manifolds. We have generalized our algorithm for presentations with three generators and a certain class of relations. For maeyen3 and maeyennaeyenkaeyen2, our generalized algorithm gives a -vertex crystallization of the closed connected orientable 3-manifold MaOE (c) m,n,k > having fundamental group . These crystallizations are minimal and unique with respect to the given presentations. If ` n=2' or ` kaeyen3 and maeyen4' then our crystallization of MaOE (c) m,n,k > is vertex-minimal for all the known cases.

Item Type:	Journal Article
Publication:	PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
Additional Information:	Copy right for this article belongs to the INDIAN ACAD SCIENCES, C V RAMAN AVENUE, SADASHIVANAGAR, P B #8005, BANGALORE 560 080, INDIA
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Dec 2016 05:54
Last Modified:	07 Dec 2016 05:54
URI:	http://eprints.iisc.ac.in/id/eprint/55546

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