Cataloguing PL 4-manifolds by gem-complexity
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 different classification in 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.
Cite
@article{arxiv.1408.0378,
title = {Cataloguing PL 4-manifolds by gem-complexity},
author = {M. R. Casali and P. Cristofori},
journal= {arXiv preprint arXiv:1408.0378},
year = {2017}
}
Comments
25 pages, 5 figures. Improvements suggested by the referee