In this paper we prove that the Steenrod operations act naturally on the negative cyclic homology of a differential
graded algebra $A$ over the prime field $Fp$ satisfying some extra conditions. When $A$ denotes the singular cochains
with coefficients in $Fp$ of a $1$-connected space $X$, these extra conditions are satisfied. The Jones isomorphism
identifies these Steenrod operations with the usual ones on the $S^1$-equivariant cohomology of the free loop
space on $X$ with coefficients in $Fp$. We conclude by performing some calculations on the negative cyclic homology.
Publié le : 2009-05-15
Classification:
Hochschild homology,
negative cyclic homology,
bar and cobar construction,
shc-algebra,
55S20,
57T30,
54C35,
13D03
@article{1251832569,
author = {Tcheka, Calvin},
title = {Steenrod operations on the negative cyclic homology of the shc-cochain algebras},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 315-348},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832569}
}
Tcheka, Calvin. Steenrod operations on the negative cyclic homology of the shc-cochain algebras. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 315-348. http://gdmltest.u-ga.fr/item/1251832569/