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Graph manifolds, left-orderability and amalgamation
We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov andExpand
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Surgery obstructions and Heegaard Floer homology
Using Taubes' periodic ends theorem, Auckly gave examples of toroidal and hyperbolic irreducible integer homology spheres which are not surgery on a knot in the three-sphere. We give an obstructionExpand
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Ribbon homology cobordisms
We study 4-dimensional homology cobordisms without 3-handles, showing that they interact nicely with Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. UsingExpand
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Rank inequalities for the Heegaard Floer homology of Seifert homology spheres
We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integral homology spheres. Combining these inequalities with the known classifications ofExpand
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APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY
Abstract We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphereExpand
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Framed instanton homology of surgeries on L-space knots
An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framedExpand
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The equivalence of two Seiberg-Witten Floer homologies
We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S^1-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author.
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Berge-Gabai knots and L-space satellite operations
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 S^3. WeExpand
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Cosmetic surgery in L-spaces and nugatory crossings
The cosmetic crossing conjecture (also known as the “nugatory crossing conjecture”) asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3-sphere areExpand
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Quasi-alternating links with small determinant
Abstract Quasi-alternating links of determinant 1, 2, 3 and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend thisExpand
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