The Anick Complex and the Hochschild Cohomology of the Manturov (2,3)-Group

The Manturov (2, 3)-group G32 is the group generated by three elements a, b, and c with defining relations a(2) = b(2) = c(2) = (abc)(2) = 1. We explicitly calculate the Anick chain complex for G32 by algebraic discrete Morse theory and evaluate the Hochschild cohomology groups of the group algebra kG32 with coefficients in all 1-dimensional bimodules over a field kof characteristic zero.