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Topological Hochschild homology of twisted group algebras

Author: Daniel J. Vera
Journal: Trans. Amer. Math. Soc. 362 (2010), 1113-1133
MSC (2000): Primary 55-xx
Published electronically: October 20, 2009
MathSciNet review: 2563723
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Abstract: We show that the topological Hochschild homology spectrum of a twisted group algebra $ \operatorname{THH}(A^{\tau}[G])$ is the Thom spectrum associated with a parametrized orthogonal spectrum $ E(A,G)$. We then analyze the structure of the parametrized orthogonal spectrum $ E(A,G)$ and show that it is locally trivial.

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  • 1. S. Araki, Coefficients of $ MR$-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 $ K$-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, $ K$-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, $ K$-theory of truncated polynomial algebras, Handbook of $ K$-theory, Springer-Verlag, New York, 2005. MR 2181821 (2006m:19005)
  • 7. L. Hesselholt and I. Madsen, On the $ K$-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 $ S$-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

Received by editor(s): June 1, 2006
Published electronically: October 20, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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