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. © 2012 World Scientific Publishing Company.

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Tange, M., & Yamada, Y. (2012). Four-dimensional manifolds constructed by lens space surgeries along torus knots. Journal of Knot Theory and Its Ramifications, 21(11). https://doi.org/10.1142/S0218216512501118

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