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OPEN BOOKS FOR CLOSED NON-ORIENTABLE 3–MANIFOLDS

Published online by Cambridge University Press:  07 October 2019

ABHIJEET GHANWAT ,
SUHAS PANDIT  and
A SELVAKUMAR
ABHIJEET GHANWAT
Affiliation:
Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, Tamilnadu, India e-mail: abhijeet@cmi.ac.in
SUHAS PANDIT
Affiliation:
Indian Institute of Technology Madras, IIT PO., Chennai, 600036, Tamilnadu, India e-mails: suhas@iitm.ac.in; ma15d010@smail.iitm.ac.in
A SELVAKUMAR
Affiliation:
Indian Institute of Technology Madras, IIT PO., Chennai, 600036, Tamilnadu, India e-mails: suhas@iitm.ac.in; ma15d010@smail.iitm.ac.in
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Abstract

In this note, we give a new proof of the existence of an open book decomposition for a closed non-orientable 3–manifold. This open book decomposition is analogous to a planar open book decomposition for a closed orientable 3–manifold. More precisely, in this note, we give an open book decomposition of a given closed non-orientable 3–manifold with the pages punctured Möbius bands. We also give an algorithm to determine the monodromy of this open book.

Keywords

57M99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 584 - 599
Copyright
© Glasgow Mathematical Journal Trust 2019

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