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Bibliographic Details
Main Authors: Hambleton, Ian, Hillman, Jonathan A.
Format: Preprint
Published: 2017
Subjects:
Online Access:https://arxiv.org/abs/1712.04572
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author Hambleton, Ian
Hillman, Jonathan A.
author_facet Hambleton, Ian
Hillman, Jonathan A.
contents We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $χ(M) = 1$. All such manifolds with $π=π_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $π\cong {\mathbb Z}/2 \times {\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types).
format Preprint
id arxiv_https___arxiv_org_abs_1712_04572
institution arXiv
publishDate 2017
record_format arxiv
spellingShingle Quotients of $S^2\times{S^2}$
Hambleton, Ian
Hillman, Jonathan A.
Geometric Topology
57M60, 57N70
We consider closed topological 4-manifolds $M$ with universal cover ${S^2\times{S^2}}$ and Euler characteristic $χ(M) = 1$. All such manifolds with $π=π_1(M)\cong {\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $π\cong {\mathbb Z}/2 \times {\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types).
title Quotients of $S^2\times{S^2}$
topic Geometric Topology
57M60, 57N70
url https://arxiv.org/abs/1712.04572