2 citations · 6 across the 10 of their papers we have counts for
11 papers
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…
The link surgery formula and equivariant surgeries
Kristen Hendricks, Abhishek Mallick, Matthew Stoffregen +1
We prove an equivariant version of the Heegaard Floer link surgery formula. As a special case, this gives an equivariant knot surgery formula for equivariant knots in . Our pr…
A note on cables and the involutive concordance invariants
Kristen Hendricks, Abhishek Mallick
We prove a formula for the involutive concordance invariants of the cabled knots in terms of that of the companion knot and the pattern knot. As a consequence, we show that any ite…
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…
Exotic Dehn twists on 4-manifolds
Hokuto Konno, Abhishek Mallick, Masaki Taniguchi
We initiate the study of exotic Dehn twists along 3-manifolds inside -manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-m…
From diffeomorphisms to exotic phenomena in small 4-manifolds
Hokuto Konno, Abhishek Mallick, Masaki Taniguchi
We provide an approach to study exotic phenomena in relatively small 4-manifolds that captures many different exotic behaviors under one umbrella. These phenomena include exotic sm…
Rank-expanding satellites, Whitehead doubles, and Heegaard Floer homology
Irving Dai, Matthew Hedden, Abhishek Mallick +1
We show that a large class of satellite operators are rank-expanding; that is, they map some rank-one subgroup of the concordance group onto an infinite linearly independent set. O…
The -cable of the figure-eight knot is not smoothly slice
Irving Dai, Sungkyung Kang, Abhishek Mallick +2
We prove that the -cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
Knot Floer homology and surgery on equivariant knots
Abhishek Mallick
Given an equivariant knot of order , we study the induced action of the symmetry on the knot Floer homology. We relate this action with the induced action of the symmetry on…
Equivariant knots and knot Floer homology
Irving Dai, Abhishek Mallick, Matthew Stoffregen
We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to gi…