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We use classical techniques to answer some questions raised by Daniele Celoria about almost-concordance of knots in arbitrary closed 3–manifolds. We first prove that, given Y 3≠S3, for any nontrivial element g ∈ π1(Y ) there are infinitely many distinct smooth almost-concordance classes in the free homotopy class of the unknot. In particular we consider these distinct smooth almost-concordance classes on the boundary of a Mazur manifold and we show none of these distinct classes bounds a PL–disk in the Mazur manifold, but all the representatives we construct are topologically slice. We also prove that all knots in the free homotopy class of S1 × pt in S1 × S2 are smoothly concordant.
Keywords: knot concordance, homology sphere, $S^1\times S^2$, almost concordance, singular concordance, PL concordance
Yildiz, Eylem 1
@article{10_2140_agt_2018_18_3119,
author = {Yildiz, Eylem},
title = {A note on knot concordance},
journal = {Algebraic and Geometric Topology},
pages = {3119--3128},
publisher = {mathdoc},
volume = {18},
number = {5},
year = {2018},
doi = {10.2140/agt.2018.18.3119},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3119/}
}
Yildiz, Eylem. A note on knot concordance. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 3119-3128. doi: 10.2140/agt.2018.18.3119
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