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The ``fundamental theorem'' for the algebraic  -theory of spaces. III. The nil-term
Author(s):
John
R.
Klein;
E.
Bruce
Williams
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3025-3033.
MSC (2000):
Primary 19D10;
Secondary 19D35
Posted:
April 29, 2008
MathSciNet review:
2407063
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Additional information
Abstract:
In this paper we identify the ``nil-terms'' for Waldhausen's algebraic  -theory of spaces functor as the reduced  -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. - [B]
- Bass, H: Algebraic
 -Theory,
Benjamin, New York, 1968. MR 0249491 (40:2736) - [F]
-
Farrell, T.: Private Communication, 2006. - [H
 ] - Hüttemann, T., Klein, J.R., Vogell, W., Waldhausen, F., Williams, B.: The ``fundamental theorem'' for the algebraic
 -theory of spaces. I.
J. Pure Appl. Algebra 160, 21-52 (2001). MR 1829311 (2002a:19003) - [H
 2] - Hüttemann, T., Klein, J.R., Vogell, W., Waldhausen, F., Williams, B.: The ``fundamental theorem'' for the algebraic
 -theory of spaces. II.
J. Pure Appl. Algebra 167, 53-82 (2002). MR 1868117 (2002i:19003) - [G]
- Grayson, D.: Higher algebraic
 -theory II (after Daniel Quillen),
Algebraic  -theory, Lecture Notes in Math., vol. 551, Springer, Berlin, 1976, pp. 217-240. MR 0574096 (58:28137) - [GKM]
- 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 - [VS]
- Schwänzl, R., Vogt, R.M.: The categories of
 - and  -monoids and ring spaces as closed simplicial and topological model categories.
Arch. Math. (Basel) 56, 405-411 (1991). MR 1094430 (92b:18006) - [W]
- Waldhausen, F.: Algebraic
 -theory of spaces.
Algebraic and Geometric Topology, Proceedings Rutgers, 1983, Lecture Notes in Math., vol. 1126, Springer, Berlin, 1985, pp. 318-419. MR 802796 (86m:18011)
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Additional Information:
John
R.
Klein
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202
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
DOI:
10.1090/S0002-9939-08-09293-9
PII:
S 0002-9939(08)09293-9
Received by editor(s):
May 7, 2007,
Received by editor(s) in revised form:
July 3, 2007
Posted:
April 29, 2008
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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