2017年10月
Four-dimensional manifolds constructed by lens space surgeries of distinct types
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- ,
- 巻
- 26
- 号
- 11
- 開始ページ
- 1750069-1
- 終了ページ
- 51
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1142/S0218216517500699
- 出版者・発行元
- WORLD SCIENTIFIC PUBL CO PTE LTD
A framed knot with an integral coefficient determines a simply-connected 4-manifold by 2-handle attachment. Its boundary is a 3-manifold obtained by Dehn surgery along the framed knot. For a pair of such Dehn surgeries along distinct knots whose results are homeomorphic, it is a natural problem: Determine the closed 4-manifold obtained by pasting the 4-manifolds along their boundaries. We study pairs of lens space surgeries along distinct knots whose lens spaces (i.e. the resulting lens spaces of the surgeries) are orientation-preservingly or -reversingly homeomorphic. In the authors' previous work, we treated with the case both knots are torus knots. In this paper, we focus on the case where one is a torus knot and the other is a Berge's knot Type VII or VIII, in a genus one fiber surface. We determine the complete list (set) of such pairs of lens space surgeries and study the closed 4-manifolds constructed as above. The list consists of six sequences. All framed links and handle calculus are indexed by integers.
- リンク情報
- ID情報
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- DOI : 10.1142/S0218216517500699
- ISSN : 0218-2165
- eISSN : 1793-6527
- Web of Science ID : WOS:000412572700009