63 citations · 205 across the 40 of their papers we have counts for
52 papers
Non-determinacy of HOMFLY-PT homology for diagrams
Maciej Borodzik, Mikhail Malashchuk
We show that for any two knots , in , there exist diagrams and that represent and , respectively, such that the Khovanov--Rozansky t…
Local equivalence via homological algebra
Maciej Borodzik
We study local equivalence of bounded complexes over a polynomial ring , where is a noetherian ring. We provide a homological algebra approach to the results, the variant…
Merging boundary critical points of a Morse function
Maciej Borodzik, Marcin Mielniczuk
In 2015, Borodzik, Némethi and Ranicki proved that an interior critical point can be pushed to the boundary, where it splits into two boundary critical points. In this paper, we sh…
Lattice homology, formality, and plumbed L-space links
Maciej Borodzik, Beibei Liu, Ian Zemke
We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth, Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in rat…
Khovanov-Rozansky -homology for periodic links
Maciej Borodzik, Wojciech Politarczyk, Ramazan Yozgyur
For an -periodic link , we show that the Khovanov-Rozansky -homology carries an action of the group . As an example of applications, we prove a…
Twisted Blanchfield pairings and twisted signatures I: Algebraic background
Maciej Borodzik, Anthony Conway, Wojciech Politarczyk
This is the first paper in a series of three devoted to studying twisted linking forms of knots and three-manifolds. Its function is to provide the algebraic foundations for the ne…