Maciej Borodzik

activity

20242026

collaborators

6 papers

math.GT2026

Reidemeister and movie moves for involutive links

Maciej Borodzik, Irving Dai, Abhishek Mallick +1

An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^{3}$ . We establish an equivariant analogue of the work of Carter and Saito aimed at s…

math.GT2025

Non-complex cobordisms between quasipositive knots

Maciej Borodzik, Paula TruÃ¶l

We show that for every genus $g \geq 0$ , there exist quasipositive knots $K_{0}^{g}$ and $K_{1}^{g}$ such that there is a cobordism of genus $g = ∣ g_{4} (K_{1}^{g}) - g_{4} (K_{0}^{g}) ∣$ between $K_{0}^{g}$ and…

math.GT2025

Families of Morse functions for manifolds with boundary

Maciej Borodzik, Weronika BuczyÅska

We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.

math.GT2025

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…

math.GT2025

Link concordance implies link homotopy

Maciej Borodzik, Mark Powell, Peter Teichner

We show that link concordance implies link homotopy for immersions of codimension at least two. As a consequence, we prove that every link $⊔^{r} S^{n} ↪ S^{n + 2}$ is…

math.GT2024

Hyperbolic L-space knots not concordant to algebraic knots

Maciej Borodzik, Masakazu Teragaito

We construct hyperbolic L-space knots that are not concordant to any linear combination of algebraic knots.