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Diagrams for Relative Trisections
We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes inExpand
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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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Trisections of 4-manifolds with boundary
Significance Trisections are decompositions of 4D spaces (4-manifolds) into three pieces; these decompositions become both richer and more subtle when the 4-manifolds have 3D boundaries and even moreExpand
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A note on the topological slice genus of satellite knots
This paper presents evidence supporting the surprising conjecture that in the topological category the slice genus of a satellite knot $P(K)$ is bounded above by the sum of the slice genera of $K$Expand
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Toroidal homology spheres and SU(2)-representations
We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible SU(2)representations. Our methods use instanton FloerExpand
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Four–manifolds and knot concordance
Topology deals with global or large-scale structures of objects. Geometric topology is the study of manifolds and its ultimate goal is the classification of manifolds within a certain frameworkExpand
Satellites of Infinite Rank in the Smooth Concordance Group
We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use $SO(3)$Expand
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Independence of Satellites of Torus Knots in the Smooth Concordance Group
The main goal of this article is to obtain a condition under which an infinite collection $\mathscr{F}$ of satellite knots (with companion a positive torus knot and pattern similar to the WhiteheadExpand
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Independence of Iterated Whitehead Doubles
A theorem of Furuta and Fintushel-Stern provides a criterion for a collection of Seifert fibred homology spheres to be independent in the homology cobordism group of oriented homology 3-spheres. InExpand
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Traceless SU(2) representations of 2-stranded tangles
Abstract Given a 2-stranded tangle T contained in a ℤ-homology ball Y, we investigate the character variety R(Y, T) of conjugacy classes of traceless SU(2) representations of π1(Y \ T). In particularExpand
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