Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Mallick, Abhishek"'
We introduce a method to detect exotic surfaces without explicitly using a smooth 4-manifold invariant or an invariant of a 4-manifold-surface pair in the construction. Our main tools are two versions of families (Seiberg-Witten) generalizations of D
Externí odkaz:
http://arxiv.org/abs/2409.07287
Autor:
Hendricks, Kristen, Mallick, Abhishek
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 iterated cable of a knot with parameters of the form (odd,1) is not smoot
Externí odkaz:
http://arxiv.org/abs/2409.02192
Autor:
Konno, Hokuto, Mallick, Abhishek
Ruberman in the 90's showed that the group of exotic diffeomorphisms of closed 4-manifolds can be infinitely generated. We provide various results on the question of when such infinite generation can localize to a smaller embedded submanifold of the
Externí odkaz:
http://arxiv.org/abs/2406.11773
Gompf showed that for $K$ in a certain family of double-twist knots, the swallow-follow operation makes $1/n$-surgery on $K \# -K$ into a cork boundary. We derive a general Floer-theoretic condition on $K$ under which this is the case. Our formalism
Externí odkaz:
http://arxiv.org/abs/2312.08258
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 the Chern-Simons filtration and is qualitatively different from previou
Externí odkaz:
http://arxiv.org/abs/2309.02309
We initiate the study of exotic Dehn twists along 3-manifolds $\neq S^3$ inside $4$-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more generally of definite 4-manifolds, and exotic diffeomor
Externí odkaz:
http://arxiv.org/abs/2306.08607
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 smooth structures on 4-manifolds with $b_2=1$, examples of strong corks,
Externí odkaz:
http://arxiv.org/abs/2304.05997
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. Our work constitutes the first systematic study of this property in the
Externí odkaz:
http://arxiv.org/abs/2209.07512
We prove that the $(2,1)$-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
Comment: 14 pages; 5 figures. Final version; to appear in Inventiones Mathematicae
Comment: 14 pages; 5 figures. Final version; to appear in Inventiones Mathematicae
Externí odkaz:
http://arxiv.org/abs/2207.14187
Autor:
Mallick, Abhishek
Given an equivariant knot $K$ of order $2$, 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 the Heegaard Floer homology of large surgeries on $K$. This surgery f
Externí odkaz:
http://arxiv.org/abs/2201.07299