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Moduli of suspension spectra

Author(s): John R. Klein
Journal: Trans. Amer. Math. Soc. 357 (2005), 489-507.
MSC (2000): Primary 55P42, 55P43; Secondary 55P40, 55P65
Posted: March 23, 2004
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Abstract: For a $1$-connected spectrum $E$, we study the moduli space of suspension spectra which come equipped with a weak equivalence to $E$. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical classification of the path components of the moduli space. Our main tool is Goodwillie's calculus of homotopy functors.

References:

[A-C-D]
Adem, A., Cohen, R.L., Dwyer, W.G.: Tate homology, homotopy fixed points and the transfer.
In: Algebraic Topology (Evanston 1988) Contemp. Math. 96, pp. 1-13.
AMS 1989 MR 90k:55012

[A-K]
Ahearn, S. T., Kuhn, N. J.: Product and other fine structure in polynomial resolutions of mapping spaces.
Algebr. Geom. Topol. 2, 1123-1150 (2002) MR 2003j:55009

[Ar]
Arone, G.: A generalization of the Snaith-type filtration.
Trans. Amer. Soc. 351, 591-647 (1999) MR 99i:55011

[B-H]
Berstein, I., Hilton, P. J.: On suspensions and comultiplications.
Topology 2, 73-82 (1963) MR 27:762
[Ba]
Bauer, K. B.: On Hopf algebra type and rational calculus decompositions.
Ph.D. thesis, University of Illinois Urbana-Champaign 2001

[C]
Carlsson, G.: Equvariant stable homotopy and Segal's Burnside ring conjecture.
Ann. of Math. 120, 189-224 (1984) MR 86f:57036

[Go1]
Goodwillie, T. G.: Calculus I, the derivative of a homotopy functor.
$K$-theory 4, 1-27 (1990) MR 92m:57027

[Go2]
Goodwillie, T. G.: Calculus II: analytic functors.
$K$-theory 5, 295-332 (1992) MR 93i:55015

[Go3]
Goodwillie, T. G.: Calculus III: Taylor series. Geom. Topol. 7, 645-711 (2003).

[Gr]
Gray, B.: Desuspension at an odd prime.
In: Algebraic topology, Aarhus 1982, Springer LNM 1051, pp. 360-370.
Springer, 1984 MR 86d:55017

[G-M]
Greenlees, J., May, J.: Generalized Tate Cohomology.
(AMS MDual calculus for functors to spectra. emoirs, Vol. 543).
AMS 1995 MR 96e:55006

[Jo]
Johnson, B.: The derivatives of homotopy theory.
Trans. Amer. Math. Soc. 347, 1295-1321 (1995) MR 96b:55012

[J-W]
Jones, J.D.S., Wegmann S.A.: Limits of stable homotopy and cohomotopy groups.
Math. Proc. Camb. Phil. Soc. 94, 473-482 (1983) MR 85b:55014

[Kl1]
Klein, J. R.: Poincaré embeddings and fiberwise homotopy theory.
Topology 38, 597-620 (1999) MR 2000b:57037

[Kl2]
Klein, J. R.: Axioms for generalized Farrell-Tate cohomology.
J. Pure Appl. Algebra 172(2-3), 225-238 (2002) MR 2003d:55006

[Ku]
Kuhn, N. J.: Suspension spectra and homology equivalences.
Trans. Amer. Math. Soc. 283, 303-313 (1984). MR 85g:55014

[L-M-S]
Lewis, L. G., May, J. P., Steinberger, M., McClure, J. E.: Equivariant Stable Homotopy Theory.
(LNM, Vol. 1213).
Springer, 1986 MR 88e:55002

[Mah]
Mahowald, M.: The metastable homotopy of $S^n$.
(Memoirs of the Amer. Math. Soc, No. 72).
Amer. Math. Soc. 1967 MR 38:5216

[Mc1]
McCarthy, R.: On $n$-excisive functors of module categories.
to appear in Math. Proc. Camb. Phil. Soc.

[Mc2]
McCarthy, R.: Dual calculus for functors to spectra. Homotopy methods in algebraic topology (Boulder, CO 1999).
(Contemp. Math. 271),
Amer. Math. Soc. 2001 MR 2002c:18009

[Mi]
Milgram, R. J.: Unstable Homotopy from the Stable Point of View.
(LNM, Vol. 368),
Springer, 1974 MR 50:1235

[Qu]
Quillen, D.: Homotopical Algebra.
(LNM, Vol. 43).
Springer, 1967 MR 36:6480

[Sc]
Schwede, S.: Spectra in model categories and applications to the algebraic cotangent complex.
J. Pure Appl. Algebra 120, 77-104 (1997) MR 98h:55027

[Wa]
Waldhausen, F.: Algebraic $K$-theory of spaces.
In: Algebraic and geometric topology, Proceedings Rutgers 1983, LNM 1126, pp. 318-419.
Springer, 1985 MR 86m:18011

[W-W]
Weiss, M., Williams, B.: Automorphisms of manifolds and algebraic $K$-theory. II.
J. Pure Appl. Algebra 62, 47-107 (1989) MR 91e:57055

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Additional Information:

John R. Klein
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: klein@math.wayne.edu

DOI: 10.1090/S0002-9947-04-03474-9
PII: S 0002-9947(04)03474-9
Received by editor(s): January 3, 2003
Received by editor(s) in revised form: July 1, 2003
Posted: March 23, 2004
Additional Notes: The author was partially supported by NSF Grant DMS-0201695
Copyright of article: Copyright 2004, American Mathematical Society

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