5 papers
The mod 2 cohomology rings of congruence subgroups in the Bianchi groups
Ethan Berkove, Grant Lakeland, Alexander Rahm +2
We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental d…
The mod 2 cohomology rings of SL\_2 of the imaginary quadratic integers
Ethan Berkove, Alexander Rahm
We establish general dimension formulae for the second page of the equivariant spectral sequence of the action of the SL\_2 groups over imaginary quadratic integers on their associ…
Automorphisms of and the Colored Cubes Puzzle
Ethan Berkove, David Cervantes Nava, Daniel Condon +1
Given a palette of six colors, a colored cube is a cube where each face is colored with exactly one color and each color appears on some face. Starting with an arbitrary collection…
Algebraic K-theory of mapping class groups
Ethan Berkove, Daniel Juan-Pineda, Qin Lu
We prove that the Fibered Isomorphism Conjecture of T. Farrell and L. Jones holds for various mapping class groups. In many cases, we explicitly calculate the lower algebraic K-gro…
The Integral Cohomology of the Bianchi Groups
Ethan Berkove
We calculate the integral cohomology ring structure for various members of the Bianchi group family. The main tools we use are the Bockstein spectral sequence and a long exact sequ…