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  Rational cobordisms and integral homology

Aceto, P., Celoria, D., & Park, J. (2020). Rational cobordisms and integral homology. Compositio Mathematica, 156(9), 1825-1845. doi:10.1112/S0010437X20007320.

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 Creators:
Aceto, Paolo1, Author           
Celoria, Daniele, Author
Park, JungHwan1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology
 Abstract: We consider the question of when a rational homology 3-sphere is rational
homology cobordant to a connected sum of lens spaces. We prove that every
rational homology cobordism class in the subgroup generated by lens spaces is
represented by a unique connected sum of lens spaces whose first homology
embeds in any other element in the same class. As a first consequence, we show
that several natural maps to the rational homology cobordism group have
infinite rank cokernels. Further consequences include a divisibility condition
between the determinants of a connected sum of 2-bridge knots and any other
knot in the same concordance class. Lastly, we use knot Floer homology combined
with our main result to obstruct Dehn surgeries on knots from being rationally
cobordant to lens spaces.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 21
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1811.01433
DOI: 10.1112/S0010437X20007320
 Degree: -

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Title: Compositio Mathematica
  Abbreviation : Compos. Math.
Source Genre: Journal
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Publ. Info: Cambridge University Press
Pages: - Volume / Issue: 156 (9) Sequence Number: - Start / End Page: 1825 - 1845 Identifier: -