Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 2
Lefschetz Open Book Embeddings of 4-Manifolds
Authors:
Abhijeet Ghanwat Tata Institute of Fundamental Research, 1st Homi Bhabha Road, Colaba, Mumbai, 400 005, India

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Suhas Pandit Indian Institute of Technology Madras, IIT PO. Chennai, 600 036, Tamil Nadu, India

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A. Selvakumar The Institute of Mathematical Sciences, Chennai, IV Cross Road, CIT Campus, Taramani, Chennai, 600 113, Tamil Nadu, India

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Pages:
142–159
Online Publication Date:
06 Jun 2022
Publication Date:
20 Jun 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01520
Keywords:
embeddings; 4-manifolds; Lefschetz open book; Lefschetz fibration
Restricted access

In this article, we define the notion of a generalized open book of a n-manifold over the k−sphere Sk , k < n. We discuss Lefschetz open book embeddings of Lefschetz open books of closed oriented 4-manifolds into the trivial open book over S2 of the 7−sphere S7 . If X is the double of a bounded achiral Lefschetz fibration over D2 , then X naturally admits a Lefschetz open book given by the bounded achiral Lefschetz fibration. We show that this natural Lefschetz open book of X admits a Lefschetz open book embedding into the trivial open book over S2 of the 7−sphere S7 .

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    A. Ghanwat and D, Pancholi . Embeddings of 4-manifolds inℂ P 3 . arXiv.2002.11299 [math.GT] (2020).

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    A. Ghanwat , S. Pandit and A. Selvakumar . Lefschetz open book decomposition of 4- manifolds (pre-print).

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    R. Gompf and A. Stipsicz . 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999.

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    A. Kupers . Lectures on diffeomorphism groups of manifolds. Version February 22, 2019.

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    W. Lickorish . A representation of orientable combinatorial three-manifolds. Ann. of Math. 76(2):531–540 (1962).

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    B. Ozbagci and A. Stipsicz . Surgery on contact 3-manifolds and Stein surfaces. Bolyai Society Mathematical Studies, 13. Springer-Verlag, Berlin; Janos Bolyai Mathematical Society, Budapest, 2004.

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    S. Pandit and A. Selvakumar . (Achiral) Lefschetz fibration embeddings of 4-manifolds. arXiv:2012.12644v7 [math.GT] (2021).

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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