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.
@article{10_37236_4749,
author = {Maria Rita Casali and Paola Cristofori},
title = {Cataloguing {PL} 4-manifolds by gem-complexity},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/4749},
zbl = {1332.57020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4749/}
}
TY - JOUR
AU - Maria Rita Casali
AU - Paola Cristofori
TI - Cataloguing PL 4-manifolds by gem-complexity
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/4749/
DO - 10.37236/4749
ID - 10_37236_4749
ER -
%0 Journal Article
%A Maria Rita Casali
%A Paola Cristofori
%T Cataloguing PL 4-manifolds by gem-complexity
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/4749/
%R 10.37236/4749
%F 10_37236_4749
Maria Rita Casali; Paola Cristofori. Cataloguing PL 4-manifolds by gem-complexity. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/4749
