4 papers
math.AT2025
Homological vanishing for the Steinberg representation II: reductive groups and integral conjectures
Jeremy Miller, Peter Patzt, Andrew Putman
We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Put…
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 and . 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 .