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Studies of distance one surgeries on the lens space L(p, 1)

Part of: Low-dimensional topology Differential topology

Published online by Cambridge University Press:  07 June 2021

ZHONGTAO WU  and
JINGLING YANG
ZHONGTAO WU
Affiliation:
Room 216, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong. e-mail: [email protected]
JINGLING YANG
Affiliation:
Room 417, Chengdao Building, The Chinese University of Hong kong, Shenzhen, 2001 Longxiang Road, Longgang District, Shenzhen City, 51800, China. e-mail: [email protected] e-mail: [email protected]
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Abstract

In this paper, we study distance one surgeries between lens spaces L(p, 1) with p ≥ 5 prime and lens spaces L(n, 1) for $$n \in \mathbb{Z}$$ and band surgeries from T (2, p) to T (2, n). In particular, we prove that L(n, 1) is obtained by a distance one surgery from L(5, 1) only if n=±1, 4, ±5, 6 or ±9, and L(n, 1) is obtained by a distance one surgery from L(7, 1) if and only if n=±1, 3, 6, 7, 8 or 11.

MSC classification

Secondary: 57R58: Floer homology 57M12: Special coverings, e.g. branched
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 2 , March 2022 , pp. 267 - 301
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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References

Boileau, M., Boyer, S., Cebanu, R. and Walsh, G. S.. Knot commensurability and the Berge conjecture. Geom. Topol. (2) 16 (2012), 625–664.CrossRefGoogle Scholar
Darcy, I. K. and Sumners, D. W.. Rational tangle distances on knots and links. Math. Proc. Camb. Phil. Soc. (3) 128 (2000), 497–510.CrossRefGoogle Scholar
Greene, J. E.. The lens space realization problem. Ann. of Math. (2) 177 (2013), 449–511.CrossRefGoogle Scholar
Lickorish, W. R.. A representation of orientable combinatorial 3-manifolds. Ann. of Math. 76 (1962), 531–540.CrossRefGoogle Scholar
Lidman, T., Moore, A. H. and Vazquez, M.. Distance one lens space fillings and band surgery on the trefoil knot. Algebr. Geom. Topol. (5) 19 (2019), 2439–2484.CrossRefGoogle Scholar
Moore, A. H. and Vazquez, M.. A note on band surgery and the signature of a knot. Bull. London Math. Soc. (6) 52 (2020), 1191–1208.CrossRefGoogle Scholar
Ni, Y. and Wu, Z.. Cosmetic surgeries on knots in S3. Reine Angew. Math. 706 (2015), 1–17.CrossRefGoogle Scholar
Ozsváth, P. and Szabó, Z.. Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary. Adv. Math. (2) 173 (2003), 179–261.CrossRefGoogle Scholar
Ozsváth, P. and Szabó, Z.. On the Floer homology of plumbed three-manifolds. Geom. Topol. (1) 7 (2003), 185–224.CrossRefGoogle Scholar
Ozsváth, P. and Szabó, Z.. Knot Floer homology and integer surgeries. Algebr. Geom. Topol. (1) 8 (2008), 101–153.CrossRefGoogle Scholar
Ozsváth, P. and Szabó, Z.. Knot Floer homology and rational surgeries. Algebr. Geom. Topol. (1) 11 (2010), 1–68.CrossRefGoogle Scholar
Rasmussen, J.. Floer homology and knot complements. Ph.D. thesis, Harvard University (2003).Google Scholar
Rasmussen, J.. Lens space surgeries and L-space homology spheres. arXiv:0710.2531 (2007).Google Scholar
Turaev, V.. Torsions of 3-dimensional manifolds. Prog. in Math. 208 (Birkhäuser Verlag, Basel, 2002).CrossRefGoogle Scholar
Wallace, A. H.. Modifications and cobounding manifolds. Canad. J. Math. 12 (1960), 503–528.CrossRefGoogle Scholar