Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Next Article
     

Twisted homology of symmetric groups

Author(s): Stanislaw Betley
Journal: Proc. Amer. Math. Soc. 130 (2002), 3439-3445.
MSC (1991): Primary 20J06; Secondary 18G99
Posted: July 2, 2002
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We study the homology of symmetric groups $\Sigma _{n}$ with coefficients coming from the functor $T:\textit{finite pointed sets }\to Ab$. We are primarily interested in the limit $co\lim _{n}H_{*}(\Sigma _{n};T([n]))$ where $[n]=\{ 0,1,...,n\}$. Our main goal is to compare the described above situation with the case of general linear groups.

References:

[B1]
S. Betley. Calculations in THH-theory. J. Algebra 180 (1996), 445-458. MR 97a:19002

[B2]
S. Betley. On stable K-theory with twisted coefficients. Contemporary Math. 199 (1996) 19-29. MR 98a:19002

[B3]
S. Betley. Homology of Gl(R) with coefficients in a functor of finite degree. J. Algebra 150 (1992) 73-86. MR 93m:20069

[B4]
S. Betley. Stable derived functors, the Steenrod algebra and homological algebra in the category of functors. Fundamenta Math. 168 (2001) 279-293. MR 2002f:18025

[BP-1]
S. Betley and T. Pirashvili. Twisted (co)homological stability for monoids of endomorphisms. Math. Ann. 295 (1993), 709-720. MR 94g:18006

[BP-2]
S. Betley and T. Pirashvili. Stable $K$-theory as a derived functor. J. of Pure and Appl. Alg. 96 (1994) 245-258. MR 96a:19002

[BS]
S. Betley and J. S\lominska. New approach to the groups $H_{*}(\Sigma _{n},Lie_{n})$ by the homology theory of the category of functors. J. Pure and App. Alg. 161 (2001) 31-43. MR 2002e:55020

[FFSS]
V. Franjou, E.M. Friedlander, A. Scorichenko and A. Suslin. General linear and functor cohomology over finite fields. Ann. of Math. 150 (1999) 663-728. MR 2001b:14076

[JP]
M. Jibladze and T. Pirashvili. Cohomology of algebraic theories. J. Algebra 137 (1991) 253-296. MR 92f:18005

[vdK]
W. van der Kallen. Homology stability for linear groups. Inventiones Math. 60 (1980) 269-295. MR 82c:18011

[K]
C. Kassel. Stabilisation de la K-theorie algebrique des espaces topologiques. Ann. Scient. Ec. Norm. Sup. 16 (1983) 123-149. MR 85j:18010

[N]
M. Nakaoka. Decomposition theorem for homology groups of symmetric groups. Ann. of Math. 71 (1960) 16-42. MR 22:2989

[P1]
T. Pirashvili. Dold-Kan type theorem for $\Gamma $-groups. Math. Ann. 318 (2000) 277-298. MR 2001i:20112

[P2]
T. Pirashvili. Hodge decomposition for higher order Hochschild homology. Ann. Scient. Ec. Norm. Sup. 33 (2000) 151-179. MR 2001e:19006

[S]
A. Scorichenko. Stable K-theory and functor homology over a ring. Preprint IAS, 2000.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20J06, 18G99

Retrieve articles in all Journals with MSC (1991): 20J06, 18G99

Additional Information:

Stanislaw Betley
Affiliation: Instytut Matematyki, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
Email: betley@mimuw.edu.pl

DOI: 10.1090/S0002-9939-02-06763-1
PII: S 0002-9939(02)06763-1
Received by editor(s): October 4, 2000
Posted: July 2, 2002
Additional Notes: The author was partially supported by the Polish Scientific Grant (KBN) 2 P03A 01113
Communicated by: Ralph Cohen
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google