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Topological Hochschild homology of twisted group algebras
Author(s):
Daniel
J.
Vera
Journal:
Trans. Amer. Math. Soc.
362
(2010),
1113-1133.
MSC (2000):
Primary 55-xx
Posted:
October 20, 2009
MathSciNet review:
2563723
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Additional information
Abstract:
We show that the topological Hochschild homology spectrum of a twisted group algebra is the Thom spectrum associated with a parametrized orthogonal spectrum . We then analyze the structure of the parametrized orthogonal spectrum and show that it is locally trivial.
References:
-
- 1.
- S. Araki, Coefficients of
-theory, Preprint, Osaka City University, Mimeographed Notes. - 2.
- M. Bökstedt, Topological Hochschild homology, Preprint, Bielefeld University, 1985.
- 3.
- M. Bökstedt, W.-C. Hsiang, and I. Madsen, The cyclotomic trace and algebraic
-theory of spaces, Invent. Math. 111 (1993), 465-540. MR 1202133 (94g:55011) - 4.
- B.L. Feıgin and B.L. Tsygan, Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras,
-theory, arithmetic and geometry (Moscow, 1984-1986), Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 210-239. MR 923137 (89c:17020) - 5.
- P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 35, Springer-Verlag, New York, 1967. MR 0210125 (35:1019)
- 6.
- L. Hesselholt,
-theory of truncated polynomial algebras, Handbook of -theory, Springer-Verlag, New York, 2005. MR 2181821 (2006m:19005) - 7.
- L. Hesselholt and I. Madsen, On the
-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), 29-102. MR 1410465 (97i:19002) - 8.
- M. Hovey, B. Shipley, and J. Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000), 149-208. MR 1695653 (2000h:55016)
- 9.
- J.-L. Loday, Cyclic homology, Grundlehren der mathematischen Wissenschaften, vol. 301, Springer-Verlag, New York, 1992. MR 1217970 (94a:19004)
- 10.
- M. A. Mandell and J. P. May, Equivariant orthogonal spectra and
-modules, Mem. Amer. Math. Soc., vol. 159, Amer. Math. Soc., Providence, RI, 2002. MR 1922205 (2003i:55012) - 11.
- J. P. May, The geometry of iterated loop spaces, Lecture Notes in Math., vol. 271, Springer-Verlag, New York, 1972. MR 0420610 (54:8623b)
- 12.
- J.P. May and J. Sigurdsson, Parametrized homotopy theory, Preprint 2004, math.AT/0411656. MR 2271789
- 13.
- C. Schlichtkrull, The transfer map in topological Hochschild homology, J. Pure Appl. Alg. 133 (1998), 289-316. MR 1654263 (99j:19003)
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Additional Information:
Daniel
J.
Vera
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
DOI:
10.1090/S0002-9947-09-04572-3
PII:
S 0002-9947(09)04572-3
Received by editor(s):
June 1, 2006
Posted:
October 20, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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