Martin Tancer

activity

20232026

collaborators

6 papers

math.CO2026

Non-acyclic spaces of line transversals

Haochi Jiang, Martin Tancer

Cheong, Goaoc and Holmsen conjectured that every connected component of the space of line transversals to a family of pairwise disjoint open convex sets in $R^{d}$ is acycli…

math.CO2026

Maximal matroids and counterexamples

Denys Bulavka, Martin Tancer

Jackson and Tanigawa conjectured that the rigidity matroid $R_{n}^{d}$ and the hyperconnectivity matroid $H_{n}^{d}$ are the unique maximal matroids in the posets of $\…

math.CO2025

A note on the computational complexity of weak saturation

Martin Tancer, Mykhaylo Tyomkyn

We prove that determining the weak saturation number of a host graph $F$ with respect to a pattern graph $H$ is already a computationally hard problem when $H$ is the triangle. As…

math.GT2024

Algorithms in 4-manifold topology

Stefan Bastl, Rhuaidi Burke, Rima Chatterjee +28

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In p…

math.CO2024

Pach's animal problem within the bounding box

Martin Tancer

A collection of unit cubes with integer coordinates in $R^{3}$ is an animal if its union is homeomorphic to the 3-ball. Pach's animal problem asks whether any animal can be t…

math.GT2023

Simpler algorithmically unrecognizable 4-manifolds

Martin Tancer

Markov proved that there exists an unrecognizable 4-manifold, that is, a 4-manifold for which the homeomorphism problem is undecidable. In this paper we consider the question how c…