Homotopy classification of 4-manifolds whose fundamental group is
dihedral
dihedral
File(s)
Accepted version
Author(s)
Kasprowski, Daniel
Nicholson, John
Ruppik, Benjamin
Type
Journal Article
Abstract
We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is
determined by its quadratic 2-type provided its fundamental group is finite and
has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck
and Bauer, this applies in the case of smooth oriented 4-manifolds whose
fundamental group is a finite subgroup of SO(3). An important class of examples
are elliptic surfaces with finite fundamental group.
determined by its quadratic 2-type provided its fundamental group is finite and
has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck
and Bauer, this applies in the case of smooth oriented 4-manifolds whose
fundamental group is a finite subgroup of SO(3). An important class of examples
are elliptic surfaces with finite fundamental group.
Date Issued
2022-12-13
Date Acceptance
2021-07-14
Citation
Algebraic and Geometric Topology, 2022, 22, pp.2915-2949
ISSN
1472-2739
Publisher
Mathematical Sciences Publishers (MSP)
Start Page
2915
End Page
2949
Journal / Book Title
Algebraic and Geometric Topology
Volume
22
Copyright Statement
© 2022 Mathematical Sciences Publishers. All rights reserved.
Identifier
http://arxiv.org/abs/2011.03520v2
Subjects
math.GT
math.GT
math.AT
57K40, 16E05, 57N65, 57P10
Notes
23 pages. Final version, to appear in Algebraic & Geometric Topology
Publication Status
Published