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 a2 = b2 = c2 = (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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{k}G_3^2$$\end{document} with coefficients in all 1-dimensional bimodules over a field k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{k}$$\end{document} of characteristic zero.