Daniel Minahan

collaborators

6 papers

math.GT2026

Rigidity of maps between configuration spaces

Rodrigo De Pool, Peter Huxford, Daniel Minahan +1

Let $n \geq 5$ and $m \geq 3$ . Let $I^¦ : B_{n} \to B_{m}$ be a homomorphism of braid groups. We prove that if the image of $I^¦$ is irreducible and not cyclic, then $m = n$ …

math.GT2025

The second rational homology of the Torelli group is finitely generated

Daniel Minahan

We prove that second rational homology of the Torelli group of an orientable closed surface of genus g is finite dimensional for g at least 51. This rules out the simplest obstruct…

math.GT2025

The acyclicity of the complex of homologous curves

Daniel Minahan

We show that the complex of homologous curves of a closed, oriented surface of genus g is (g-3)--acyclic.

math.RT2025

Presentations of representations

Daniel Minahan, Andrew Putman

We give a new technique for constructing presentations by generators and relations for representations of groups like $S L_{n} (Z)$ and $S p_{2 g} (Z)$ . Our results play…

math.GT2025

Abelian covers of surfaces and the homology of the Torelli group

Daniel Minahan, Andrew Putman

We study the first homology group of the mapping class group and Torelli group with coefficients in the first rational homology group of the universal abelian cover of the surface.…

math.GT2025

The second rational homology of the Torelli group

Daniel Minahan, Andrew Putman

We calculate the second rational homology group of the Torelli group for $g \geq 6$ .