Doubles without open book decompositions from higher signatures

Fuente: arXiv
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Main Author: Kotschick, D.
Format: Preprint
Published: 2025
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author Kotschick, D.
author_facet Kotschick, D.
contents We show that in every even dimension there are closed manifolds that are doubles, but have no open book decomposition. In high dimensions, this contradicts the conclusions in Ranicki's book on high-dimensional knot theory. In all dimensions, examples arise from the non-multiplicativity of the signature in fibre bundles. We discuss many examples and applications in dimension four, where this phenomenon is related to the simplicial volume.
format Preprint
id arxiv_https___arxiv_org_abs_2510_24995
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Doubles without open book decompositions from higher signatures
Kotschick, D.
Geometric Topology
Symplectic Geometry
57R15
We show that in every even dimension there are closed manifolds that are doubles, but have no open book decomposition. In high dimensions, this contradicts the conclusions in Ranicki's book on high-dimensional knot theory. In all dimensions, examples arise from the non-multiplicativity of the signature in fibre bundles. We discuss many examples and applications in dimension four, where this phenomenon is related to the simplicial volume.
title Doubles without open book decompositions from higher signatures
topic Geometric Topology
Symplectic Geometry
57R15
url https://arxiv.org/abs/2510.24995