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A NOTE ON OPEN BOOK EMBEDDINGS OF $3$-MANIFOLDS IN $\boldsymbol {S}^5$

Part of: Differential topology

Published online by Cambridge University Press:  04 October 2021

SUHAS PANDIT Open the ORCID record for SUHAS PANDIT [Opens in a new window]  and
SELVAKUMAR A Open the ORCID record for SELVAKUMAR A [Opens in a new window]
SUHAS PANDIT
Affiliation:
Department of Mathematics, Indian Institute of Technology Madras, IIT PO, Chennai 600 036, Tamil Nadu, India e-mail: suhas@iitm.ac.in
SELVAKUMAR A*
Affiliation:
The Institute of Mathematical Sciences, Chennai, IV Cross Road, CIT Campus, Taramani, Chennai 600 113, Tamil Nadu, India
*
e-mail: aselvammaths@gmail.com
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Abstract

In this note, we show that given a closed connected oriented $3$ -manifold M, there exists a knot K in M such that the manifold $M'$ obtained from M by performing an integer surgery admits an open book decomposition which embeds into the trivial open book of the $5$ -sphere $S^5.$

Keywords

open bookembedding

MSC classification

Primary: 57R40: Embeddings
Secondary: 57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) 57R65: Surgery and handlebodies
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 499 - 506
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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