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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: ztwu@math.cuhk.edu.hk
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: yangjinglingm@gmail.com e-mail: yangjingling@cuhk.edu.cn
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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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