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Creators/Authors contains: "Levine, Adam Simon"

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  1. ; (, Quantum Topology)
    Full Text Available 
  2. (, New York journal of mathematics)
    Kawauchi proved that every strongly negative amphichiral knot K in S^3 bounds a smoothly embedded disk in some rational homology ball V_K, whose construction a priori depends on K. We show that V_K is independent of K up to diffeomorphism. Thus, a single 4-manifold, along with connected sums thereof, accounts for all known examples of knots that are rationally slice but not slice. 
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    Accepted Manuscript Full Text Available
  3. ; (, Forum of Mathematics, Sigma)
    We construct infinitely many compact, smooth 4-manifolds which are homotopy equivalent to $$S^{2}$$ but do not admit a spine (that is, a piecewise linear embedding of $$S^{2}$$ 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. 
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  4. ; (, Bulletin of the London Mathematical Society)
  5. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    null (Ed.)
    Abstract We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in the 3-sphere never produces an L-space. The proof uses bordered Floer homology. 
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  6. ; ; ; ; (, Bulletin of the London Mathematical Society)