M. Mroczkowski

activity

20022021

most citedLink diagrams in Seifert manifolds and applications to skein modules

9 citations · 15 across the 8 of their papers we have counts for

collaborators

9 papers

math.GT2021

Infinitely many roots of unity are zeros of some Jones polynomials

Maciej Mroczkowski

Let $N = 2 n^{2} - 1$ or $N = n^{2} + n - 1$ , for any $n \geq 2$ . Let $M = \frac{N - 1}{2}$ . We construct families of prime knots with Jones polynomials $(- 1)^{M} \sum_{k = - M}^{M} (- 1)^{k} t^{k}$ . Such polynomi…

math.GT2020

On two crossing numbers of algebraic knots under Hopf fibration

Maciej Mroczkowski

We answer a question posed by Fielder in [1] concerning two notions of crossing number for algebraic knots $K$ under Hopf fibration, one topological, denoted $h (K)$ , the other comi…

math.GT2019

On some moves on links and the Hopf crossing number

Maciej Mroczkowski

We consider arrow diagrams of links in $S^{3}$ and define $k$ -moves on such diagrams, for any $k \in N$ . We study the equivalence classes of links in $S^{3}$ up to $k$ -moves. For…

math.GT2019★ 1 cited

Knots with Hopf crossing number at most one

Maciej Mroczkowski

We consider diagrams of links in $S^{2}$ obtained by projection from $S^{3}$ with the Hopf map and the minimal crossing number for such diagrams. Knots admitting diagrams with at most…

math.GN2018★ 9 cited

Link diagrams in Seifert manifolds and applications to skein modules

Boštjan Gabrovšek, Maciej Mroczkowski

In this survey paper we present results about link diagrams in Seifert manifolds using arrow diagrams, starting with link diagrams in $F \times S^{1}$ and $N \times^S^{1}$ , where $F…

math.GT2010

Kauffman bracket skein module of the connected sum of two projective spaces

Maciej Mroczkowski

Diagrams and Reidemeister moves for links in a twisted S^1-bundle over an unorientable surface are introduced. Using these diagrams, we compute the Kauffman Bracket Skein Module (K…