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This article is cited in 2 scientific papers (total in 2 papers)
A spectral sequence for homology of invariant group chains
Rolando Jimeneza, Angelina López Madrigala, Quitzeh Morales Meléndezb a Instituto de Matemáticas, Unidad Oaxaca, Universidad Nacional Autónoma de México, León 2, 68000 Oaxaca de Juárez, Oaxaca, México
b CONACYT — Universidad Pedagógica Nacional, unidad 201 Camino a la Zanjita S/N, Col. Noche Buena, Santa Cruz Xoxocotlán, Oaxaca. C.P. 71230
Abstract:
Let $Q$ be a finite group acting on a group $G$ by group automorphisms, $C(G)$ the bar complex and $H^Q_*(G,A)$ the homology of invariant group chains defined in K. Knudson's paper “The homology of invariant group chains”. In this paper we construct a spectral sequence converging to $H_*(Q,C(G)\otimes A)$ whose second term is isomorphic to $H^Q_*(G,A)$ for some coefficients. When this spectral sequence collapses this yields an isomorphism $H^Q_*(G,A)\cong H_*(Q,C(G)\otimes A)$, which we use to compute this homology for some cases. The construction uses a decomposition of the bar complex $C_*(G) $ in terms of the induction from some isotropy groups to the group $Q$. We also decompose the subcomplex of invariants $C_*(G)^Q$ by $Q$-orbits and use this to compute the invariant $1$-homology $H^Q_1(G,\mathbb Z)$ for some cases.
Key words and phrases:
bar complex, homology of invariant group chains, spectral sequences.
Citation:
Rolando Jimenez, Angelina López Madrigal, Quitzeh Morales Meléndez, “A spectral sequence for homology of invariant group chains”, Mosc. Math. J., 18:1 (2018), 149–162
Linking options:
https://www.mathnet.ru/eng/mmj666 https://www.mathnet.ru/eng/mmj/v18/i1/p149
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Abstract page: | 388 | References: | 36 |
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