6 papers · 1 filter
Exotic disks and singular instanton Floer homology
Irving Dai, Abhishek Mallick, Masaki Taniguchi
We show that singular instanton Floer homology with the Chern--Simons filtration can be used to produce exotic pairs of slice disks. We moreover construct a strongly invertible $\m…
Reidemeister and movie moves for involutive links
Maciej Borodzik, Irving Dai, Abhishek Mallick +1
An involutive link is a link which is invariant under the standard rotation by 180 degrees in . We establish an equivariant analogue of the work of Carter and Saito aimed at s…
Khovanov homology and equivariant surfaces
Maciej Borodzik, Irving Dai, Abhishek Mallick +1
We introduce a refinement of Bar-Natan homology for involutive links, extending the work of Lobb-Watson and Sano. We construct a new suite of numerical invariants and derive bounds…
-disks in
Anthony Conway, Irving Dai, Maggie Miller
We study locally flat disks in with boundary a fixed knot and whose complement has fundamental group $\mathbb…
Gompf's cork and Heegaard Floer homology
Irving Dai, Abhishek Mallick, Ian Zemke
Gompf showed that for in a certain family of double-twist knots, the swallow-follow operation makes -surgery on into a cork boundary. We derive a general Floer-t…
Involutions and the Chern-Simons filtration in instanton Floer homology
Antonio Alfieri, Irving Dai, Abhishek Mallick +1
Building on the work of Nozaki, Sato and Taniguchi, we develop an instanton-theoretic invariant aimed at studying strong corks and equivariant bounding. Our construction utilizes t…