Longitude surgery on genus $1$ knots
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- by Howard Lambert PDF
- Proc. Amer. Math. Soc. 63 (1977), 359-362 Request permission
Abstract:
Let $l(K)$ be the closed 3-manifold obtained by longitude surgery on the knot manifold K. Let C be the cube with holes obtained by removing an open regular neighborhood of a minimal spanning surface in K. The main result of this paper is that if K is of genus 1 and the longitude of K is in each term of the lower central series for ${\Pi _1}(C)$, then $l(K)$ is not homeomorphic to the connected sum of ${S^1} \times {S^2}$ and a homotopy 3-sphere. In particular, this implies we cannot obtain the connected sum of ${S^1} \times {S^2}$ and a homotopy 3-sphere by longitude surgery on any pretzel knot of genus 1.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 359-362
- MSC: Primary 55A25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0438322-8
- MathSciNet review: 0438322