Simple crystallizations of 4-manifolds

Basak, Biplab and Spreer, Jonathan (2016) Simple crystallizations of 4-manifolds. Advances in Geometry, 16 1: 111-130. doi:10.1515/advgeom-2015-0043

Author Basak, Biplab
Spreer, Jonathan
Title Simple crystallizations of 4-manifolds
Journal name Advances in Geometry   Check publisher's open access policy
ISSN 1615-715X
Publication date 2016-01
Sub-type Article (original research)
DOI 10.1515/advgeom-2015-0043
Open Access Status Not Open Access
Volume 16
Issue 1
Start page 111
End page 130
Total pages 20
Place of publication Berlin, Germany
Publisher Walter de Gruyter GmbH
Collection year 2017
Language eng
Formatted abstract
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, S2 × S2, 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.
Keyword (Simple) crystallizations
Intersection form
Pseudotriangulations of manifolds
Simply connected 4-manifolds
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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