9 citations · 21 across the 8 of their papers we have counts for
10 papers · 1 filter
Torres-type formulas for link signatures
David Cimasoni, Maciej Markiewicz, Wojciech Politarczyk
We investigate the limits of the multivariable signature function of a -component link as some variable tends to via two different approaches: a three-dimensional…
On the slice genus of generalized algebraic knots
Maria Marchwicka, Wojciech Politarczyk
We give examples of a linear combination of algebraic knots and their mirrors that are algebraically slice, but whose topological and smooth four-genus is two. Our examples general…
A new polynomial criterion for periodic knots
Maciej Markiewicz, Wojciech Politarczyk
The purpose of this paper is to present a new periodicity criterion. For that purpose, we study the HOMFLY-PT polynomial and the Kauffman polynomial of cables of periodic links. Fu…
Non-slice linear combinations of iterated torus knots
Anthony Conway, Min Hoon Kim, Wojciech Politarczyk
In 1976, Rudolph asked whether algebraic knots are linearly independent in the knot concordance group. This paper uses twisted Blanchfield pairings to answer this question in the a…
Khovanov homotopy type, periodic links and localizations
Maciej Borodzik, Wojciech Politarczyk, Marithania Silvero
Given an -periodic link , we show that the Khovanov spectrum constructed by Lipshitz and Sarkar admits a homology group action. We relate the Borel…
Khovanov homology and periodic links
Maciej Borodzik, Wojciech Politarczyk
Based on the results of the second author, we define an equivariant version of Lee and Bar-Natan homology for periodic links and show that there exists an equivariant spectral sequ…
Equivariant Jones Polynomials of periodic links
Wojciech Politarczyk
This paper continues the study of periodic links started in \cite{Politarczyk2}. It contains a study of the equivariant analogues of the Jones polynomial, which can be obtained fro…
Equivariant Khovanov Homology of Periodic Links
Wojciech Politarczyk
The purpose of this paper is to construct and study equivariant Khovanov homology - a version of Khovanov homology theory for periodic links. Since our construction works regardles…
4-manifolds, surgery on loops and geometric realization of Tietze transformations
Wojciech Politarczyk
In the paper \cite{wall_1}, C.T.C. Wall proved that two smooth closed simply connected 4-manifolds which are homeomorphic are in fact stably diffeomorphic. We prove a similar resul…
Stable classification of 4-manifolds obtained by the surgery on loops
Wojciech Politarczyk
This paper is concerned with the problem of stable diffeomorphism classification of 4-manifolds obtained using the surgery on loops. The main theorem states that under the assumpti…