tate homology
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Author(s):  
Rolando Jimenez ◽  
Angelina López Madrigal

Let [Formula: see text] be a finite group acting on a group [Formula: see text] as a group automorphisms, [Formula: see text] the bar complex, [Formula: see text] the homology of invariant group chains and [Formula: see text] the cohomology invariant, both defined in Knudson’s paper “The homology of invariant group chains”. In this paper, we define the Tate homology of invariants [Formula: see text] and the Tate cohomology of invariants [Formula: see text]. When the coefficient [Formula: see text] is the abelian group of the integers, we proved that these groups are isomorphics, [Formula: see text]. Further, we prove that the homology and cohomology of invariant group chains are duals, [Formula: see text], [Formula: see text].


2018 ◽  
Vol 44 (2) ◽  
pp. 329-340
Author(s):  
Pengju Ma ◽  
Renyu Zhao ◽  
Xiaoqiang Luo
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2018 ◽  
Vol 46 (8) ◽  
pp. 3334-3350 ◽  
Author(s):  
Zhenxing Di ◽  
Zhongkui Liu ◽  
Xiaoxiang Zhang

2017 ◽  
Vol 40 (1) ◽  
pp. 1-15
Author(s):  
Yanping Liu ◽  
Zhongkui Liu ◽  
Xiaoyan Yang
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2016 ◽  
Vol 32 (7) ◽  
pp. 831-844 ◽  
Author(s):  
Yan Ping Liu ◽  
Zhong Kui Liu ◽  
Xiao Yan Yang
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2016 ◽  
Vol 44 (4) ◽  
pp. 679-695 ◽  
Author(s):  
Chelliah Selvaraj ◽  
Vasudevan Biju ◽  
Ramalingam Udhayakumar
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2016 ◽  
Vol 112 (1) ◽  
pp. 169-205 ◽  
Author(s):  
Peter Albers ◽  
Kai Cieliebak ◽  
Urs Frauenfelder
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2015 ◽  
Vol 219 (3) ◽  
pp. 464-481 ◽  
Author(s):  
Lars Winther Christensen ◽  
David A. Jorgensen
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2015 ◽  
Vol 7 (4) ◽  
pp. 309-324
Author(s):  
C. Selvaraj ◽  
R. Udhayakumar
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