We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n = 4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices). Possible interactions with the (not completely known) relationship among the different classications in the TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.

Cataloguing PL 4-manifolds by gem-complexity / Casali, Maria Rita; Cristofori, Paola. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - ELETTRONICO. - 22:4(2015), pp. 1-25.

Cataloguing PL 4-manifolds by gem-complexity

CASALI, Maria Rita;CRISTOFORI, Paola
2015

Abstract

We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n = 4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices). Possible interactions with the (not completely known) relationship among the different classications in the TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.
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Cataloguing PL 4-manifolds by gem-complexity / Casali, Maria Rita; Cristofori, Paola. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - ELETTRONICO. - 22:4(2015), pp. 1-25.
Casali, Maria Rita; Cristofori, Paola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1073860
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