We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that h-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.
Daniel Kasprowski
1
;
Mark Powell
2
;
Arunima Ray
3
1
University of Southampton, UK
2
University of Glasgow, UK
3
Max-Planck-Institut für Mathematik, Bonn, Germany
Daniel Kasprowski; Mark Powell; Arunima Ray. Counterexamples in 4-manifold topology. EMS surveys in mathematical sciences, Tome 9 (2022) no. 1, pp. 193-249. doi: 10.4171/emss/56
@article{10_4171_emss_56,
author = {Daniel Kasprowski and Mark Powell and Arunima Ray},
title = {Counterexamples in 4-manifold topology},
journal = {EMS surveys in mathematical sciences},
pages = {193--249},
year = {2022},
volume = {9},
number = {1},
doi = {10.4171/emss/56},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/56/}
}
TY - JOUR
AU - Daniel Kasprowski
AU - Mark Powell
AU - Arunima Ray
TI - Counterexamples in 4-manifold topology
JO - EMS surveys in mathematical sciences
PY - 2022
SP - 193
EP - 249
VL - 9
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/emss/56/
DO - 10.4171/emss/56
ID - 10_4171_emss_56
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%J EMS surveys in mathematical sciences
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%U http://geodesic.mathdoc.fr/articles/10.4171/emss/56/
%R 10.4171/emss/56
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