Knot Complement Problem for L-space $\mathbb{Z} HS^3$

Huygens C. Ravelomanana

doi:10.1142/s0218216522500286

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arXiv · 1505.00239

Knot Complement Problem for L-space $\mathbb{Z} HS^3$

Huygens C. Ravelomanana

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Abstract

In this paper we look at the knot complement problem for L-space $\mathbb{Z}$-homology spheres. We show that an L-space $\mathbb{Z}$-homology sphere $Y$ cannot be obtained as a non-trivial surgery along a knot $K\subset Y$. As a consequence, we prove that knots in an L-space $\mathbb{Z}$-homology sphere are determined by their complements.

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BibTeX RIS

Huygens C. Ravelomanana. 2015-05-01. Knot Complement Problem for L-space $\mathbb{Z} HS^3$. https://doi.org/10.1142/s0218216522500286

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