Browsing by Author "Lidman, T"

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    Berge–Gabai knots and L–space satellite operations
    (Algebraic & Geometric Topology, 2015-01-15) Hom, J; Lidman, T; Vafaee, F
    © 2014 Mathematical Sciences Publishers. All rights reserved. Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [13] and Hom [17].
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    SIMPLY CONNECTED, SPINELESS 4-MANIFOLDS
    (Forum of Mathematics, Sigma, 2019-01-01) Levine, AS; Lidman, T
    © 2019 The Author(s). We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to S2 but do not admit a spine (that is, a piecewise linear embedding of S2 that realizes the homotopy equivalence). This is the remaining case in the existence problem for codimension-2 spines in simply connected manifolds. The obstruction comes from the Heegaard Floer d invariants.