The “fundamental theorem” for the algebraic $K$-theory of spaces. III. The nil-term
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- by John R. Klein and E. Bruce Williams PDF
- Proc. Amer. Math. Soc. 136 (2008), 3025-3033 Request permission
Abstract:
In this paper we identify the “nil-terms” for Waldhausen’s algebraic $K$-theory of spaces functor as the reduced $K$-theory of a category of equivariant spaces equipped with a homotopically nilpotent endomorphism.References
- Nil Phenomena in Topology, Workshop at Vanderbilt University, Nashville, Tennessee, April 14-15, 2007.
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- Farrell, T.: Private Communication, 2006.
- Thomas Hüttemann, John R. Klein, Wolrad Vogell, Friedhelm Waldhausen, and Bruce Williams, The “fundamental theorem” for the algebraic $K$-theory of spaces. I, J. Pure Appl. Algebra 160 (2001), no. 1, 21–52. MR 1829311, DOI 10.1016/S0022-4049(00)00058-X
- Thomas Hüttemann, John R. Klein, Wolrad Vogell, Friedhelm Waldhausen, and Bruce Williams, The “fundamental theorem” for the algebraic $K$-theory of spaces. II. The canonical involution, J. Pure Appl. Algebra 167 (2002), no. 1, 53–82. MR 1868117, DOI 10.1016/S0022-4049(01)00067-6
- Daniel Grayson, Higher algebraic $K$-theory. II (after Daniel Quillen), Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Lecture Notes in Math., Vol. 551, Springer, Berlin, 1976, pp. 217–240. MR 0574096
- Grunewald, J., Klein, J.R., Macko, T.: Operations on the A-theoretic nil-terms, submitted to Jour. of Topology, http://arxiv.org/pdf/math/0702580
- R. Schwänzl and R. M. Vogt, The categories of $A_\infty$- and $E_\infty$-monoids and ring spaces as closed simplicial and topological model categories, Arch. Math. (Basel) 56 (1991), no. 4, 405–411. MR 1094430, DOI 10.1007/BF01198229
- Friedhelm Waldhausen, Algebraic $K$-theory of spaces, Algebraic and geometric topology (New Brunswick, N.J., 1983) Lecture Notes in Math., vol. 1126, Springer, Berlin, 1985, pp. 318–419. MR 802796, DOI 10.1007/BFb0074449
Additional Information
- John R. Klein
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- MR Author ID: 308817
- Email: klein@math.wayne.edu
- E. Bruce Williams
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- Email: williams.4@nd.edu
- Received by editor(s): May 7, 2007
- Received by editor(s) in revised form: July 3, 2007
- Published electronically: April 29, 2008
- Communicated by: Paul Goerss
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3025-3033
- MSC (2000): Primary 19D10; Secondary 19D35
- DOI: https://doi.org/10.1090/S0002-9939-08-09293-9
- MathSciNet review: 2407063