FOUR-DIMENSIONAL MANIFOLDS CONSTRUCTED BY LENS SPACE SURGERIES ALONG TORUS KNOTS

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Abstract

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 determine the complete list (set) of pairs of integral surgeries along distinct torus knots whose resulting manifolds are orientation preserving/reversing homeomorphic lens spaces, and study the closed 4-manifolds constructed as above. The list consists of five sequences. All framed links and Kirby calculus are indexed by integers. As a bi-product, some sequences of embeddings of lens spaces into the standard 4-manifolds are constructed.

Journal

  • Journal of knot theory and its ramifications

    Journal of knot theory and its ramifications 21(11), 1250111, 2012-10

    World Scientific Publishing

Keywords

Codes

  • NII Article ID (NAID)
    120004945390
  • NII NACSIS-CAT ID (NCID)
    AA10833085
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0218-2165
  • Data Source
    IR 
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