The Arone–Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes
Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 127-169
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at an odd prime.

DOI : 10.2140/agt.2013.13.127
Classification : 55P65, 55S10, 55T99
Keywords: Topological realization, Calculus of functors, Unstable modules

Büscher, Sebastian  1   ; Hebestreit, Fabian  2   ; Röndigs, Oliver  1   ; Stelzer, Manfred  1

1 Institut für Mathematik, Universität Osnabrück, D-D-49069, Osnabrück, Germany
2 Mathematisches Institut, Universität Münster, D-D-48149, Münster, Germany
@article{10_2140_agt_2013_13_127,
     author = {B\"uscher, Sebastian and Hebestreit, Fabian and R\"ondigs, Oliver and Stelzer, Manfred},
     title = {The {Arone{\textendash}Goodwillie} spectral sequence for {\ensuremath{\Sigma}\ensuremath{\infty}\ensuremath{\Omega}n} and topological realization at odd primes},
     journal = {Algebraic and Geometric Topology},
     pages = {127--169},
     year = {2013},
     volume = {13},
     number = {1},
     doi = {10.2140/agt.2013.13.127},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.127/}
}
TY  - JOUR
AU  - Büscher, Sebastian
AU  - Hebestreit, Fabian
AU  - Röndigs, Oliver
AU  - Stelzer, Manfred
TI  - The Arone–Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes
JO  - Algebraic and Geometric Topology
PY  - 2013
SP  - 127
EP  - 169
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.127/
DO  - 10.2140/agt.2013.13.127
ID  - 10_2140_agt_2013_13_127
ER  - 
%0 Journal Article
%A Büscher, Sebastian
%A Hebestreit, Fabian
%A Röndigs, Oliver
%A Stelzer, Manfred
%T The Arone–Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes
%J Algebraic and Geometric Topology
%D 2013
%P 127-169
%V 13
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.127/
%R 10.2140/agt.2013.13.127
%F 10_2140_agt_2013_13_127
Büscher, Sebastian; Hebestreit, Fabian; Röndigs, Oliver; Stelzer, Manfred. The Arone–Goodwillie spectral sequence for Σ∞Ωn and topological realization at odd primes. Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 127-169. doi: 10.2140/agt.2013.13.127

[1] S T Ahearn, N J Kuhn, Product and other fine structure in polynomial resolutions of mapping spaces, Algebr. Geom. Topol. 2 (2002) 591

[2] G Arone, A generalization of Snaith-type filtration, Trans. Amer. Math. Soc. 351 (1999) 1123

[3] C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805

[4] J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973)

[5] R Bott, H Samelson, On the Pontryagin product in spaces of paths, Comment. Math. Helv. 27 (1953) 320

[6] A K Bousfield, On the homology spectral sequence of a cosimplicial space, Amer. J. Math. 109 (1987) 361

[7] R R Bruner, J P May, J E Mcclure, M Steinberger, H∞ ring spectra and their applications, 1176, Springer (1986)

[8] F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, 533, Springer (1976)

[9] G Gaudens, L Schwartz, Applications depuis K(Z∕p,2) et une conjecture de N. Kuhn, preprint (2010)

[10] T G Goodwillie, Calculus, I : The first derivative of pseudoisotopy theory, K-Theory 4 (1990) 1

[11] T G Goodwillie, Calculus, II : Analytic functors, K-Theory 5 (1992) 295

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

[13] J R Harper, Secondary cohomology operations, 49, American Mathematical Society (2002)

[14] S O Kochman, Symmetric Massey products and a Hirsch formula in homology, Trans. Amer. Math. Soc. 163 (1972) 245

[15] D Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966) 431

[16] N J Kuhn, On topologically realizing modules over the Steenrod algebra, Ann. of Math. 141 (1995) 321

[17] N J Kuhn, Stable splittings and the diagonal, from: "Homotopy methods in algebraic topology" (editors J P C Greenlees, R R Bruner, N Kuhn), Contemp. Math. 271, Amer. Math. Soc. (2001) 169

[18] N Kuhn, Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology, Algebr. Geom. Topol. 8 (2008) 2109

[19] L G Lewis Jr., J P May, M Steinberger, J E Mcclure, Equivariant stable homotopy theory, 1213, Springer (1986)

[20] J P May, A general algebraic approach to Steenrod operations, from: "The Steenrod algebra and its applications" (editor F P Peterson), Lecture Notes in Mathematics 168, Springer (1970) 153

[21] J P May, The geometry of iterated loop spaces, 271, Springer (1972)

[22] J P May, What precisely are E∞ ring spaces and E∞ ring spectra ?, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16, Geom. Topol. Publ., Coventry (2009) 215

[23] L Schwartz, À propos de la conjecture de non-réalisation due à N. Kuhn, Invent. Math. 134 (1998) 211

[24] L Schwartz, Erratum to : La conjecture de non réalisation due à N. Kuhn, Invent. Math. 182 (2010) 449

[25] L Smith, Lectures on the Eilenberg–Moore spectral sequence, 134, Springer (1970)

[26] N P Strickland, Morava E-theory of symmetric groups, Topology 37 (1998) 757

[27] N P Strickland, P R Turner, Rational Morava E-theory and DS0, Topology 36 (1997) 137

[28] R J Wellington, The unstable Adams spectral sequence for free iterated loop spaces, Mem. Amer. Math. Soc. 36 (1982)

[29] G W Whitehead, Elements of homotopy theory, 61, Springer (1978)

Cité par Sources :