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Handle decompositions of rational homology balls and Casson-Gordon invariants

Authors: Paolo Aceto, Marco Golla and Ana G. Lecuona
Journal: Proc. Amer. Math. Soc. 146 (2018), 4059-4072
MSC (2010): Primary 57N70, 57M25, 57M27
Published electronically: June 11, 2018
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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.

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Additional Information

Paolo Aceto
Affiliation: Max-Planck-Institut für Mathematik, Bonn, Germany

Marco Golla
Affiliation: Mathematical Institute, University of Oxford, United Kingdom
Address at time of publication: CNRS, Laboratoire des mathématiques Jean Leray, Université de Nantes, France

Ana G. Lecuona
Affiliation: Aix Marseille University, CNRS, Centrale Marseille, I2M, Marseille, France

Received by editor(s): July 5, 2017
Received by editor(s) in revised form: November 19, 2017
Published electronically: June 11, 2018
Additional Notes: 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.
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society