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Handle decompositions of rational homology balls and Casson–Gordon invariants

Aceto, P., Golla, M. and Lecuona, A. G. (2018) Handle decompositions of rational homology balls and Casson–Gordon invariants. Proceedings of the American Mathematical Society, 146(9), pp. 4059-4072. (doi: 10.1090/proc/14035)

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Abstract

Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds which also lead to lower bounds on the fusion number of ribbon knots. We use Levine-Tristram signatures to compute these bounds and produce explicit examples.

Item Type:Articles
Additional Information:The first author was supported by the ERC Advanced Grant LDTBud. The second author acknowledges support from the Alice and Knut Wallenberg Foundation and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 674978). The third author was partially supported by the Spanish GEOR MTM2011-22435.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Garcia Lecuona, Professor Ana
Authors: Aceto, P., Golla, M., and Lecuona, A. G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the American Mathematical Society
Publisher:American Mathematical Society
ISSN:0002-9939
ISSN (Online):1088-6826
Published Online:11 June 2018
Copyright Holders:Copyright © 2018 American Mathematical Society
First Published:First published in Proceedings of the American Mathematical Society 146(9): 4059-4072
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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