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Simple crystallizations of 4-manifolds

Basak, Biplab and Spreer, Jonathan (2016) Simple crystallizations of 4-manifolds. In: ADVANCES IN GEOMETRY, 16 (1). pp. 111-130.

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Official URL: http://dx.doi.org/10.1515/advgeom-2015-0043


Minimal crystallizations of simply connected PL 4-manifolds are very natural objects. Many of their topological features are reflected in their combinatorial structure which, in addition, is preserved under the connected sum operation. We present a minimal crystallization of the standard PL K3 surface. In combination with known results this yields minimal crystallizations of all simply connected PL 4-manifolds of ``standard'' type, that is, all connected sums of CP2, S-2 x S-2, and the K3 surface. In particular, we obtain minimal crystallizations of a pair of homeomorphic but non-PL-homeomorphic 4-manifolds. In addition, we give an elementary proof that the minimal 8-vertex crystallization of CP2 is unique and its associated pseudotriangulation is related to the 9-vertex combinatorial triangulation of CP2 by the minimum of four edge contractions.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WALTER DE GRUYTER GMBH, GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Keywords: Pseudotriangulations of manifolds; (simple) crystallizations; intersection form; simply connected 4-manifolds
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 17 Feb 2016 05:23
Last Modified: 17 Feb 2016 05:23
URI: http://eprints.iisc.ac.in/id/eprint/53234

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