The Manturov (3, 4)-group G43 is the group generated by four elements a, b, c, d with defining relations a2 = b2 = c2 = d2 = (abcd)2 = (acdb)2 = (adbc)2 = 1. We apply the algebraic discrete Morse theory to calculate the Anick chain complex for G43, evaluate the Hochschild cohomology groups of the group algebra 𝕜G43 with coefficients in all 1-dimensional bimodules over a field 𝕜 of characteristic zero, and derive its Hilbert and Poincare series.

中文翻译：

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Manturov (3,4)-群的 Anick 复数、Hochschild 上同调、Hilbert 和 Poincare 级数

曼图罗夫(3, 4)-团体G43是由四个元素生成的组一种,b,C,d定义关系一种2 = b2 = C2 = d2 = (一种bCd)2 = (一种Cdb)2 = (一种dbC)2 = 1. 我们应用代数离散莫尔斯理论来计算 Anick 链复数G43, 评估群代数的 Hochschild 上同调群𝕜G43具有域上所有一维双模中的系数𝕜零特征，并推导出其希尔伯特和庞加莱级数。