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Minimal triangulation, complementarity and projective planes

Datta, B (1997) Minimal triangulation, complementarity and projective planes. In: Pacific Rim Geometry Conference, Dec 12-17, 1994, Singapore, Singapore.

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Abstract

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

Item Type: Conference Paper
Additional Information: Copyright of this article belongs to Walter de Gruyter GmbH & Co. KG.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 15 Mar 2012 07:46
Last Modified: 15 Mar 2012 07:46
URI: http://eprints.iisc.ernet.in/id/eprint/43981

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