Geodesic
Stable and unstable operations in mod p cohomology theories
Stacey, Andrew1 ; Whitehouse, Sarah2
1Institutt for Matematiske fag, NTNU, 7491 Trondheim, Norway
2Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1059-1091
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We consider operations between two multiplicative, complex orientable cohomology theories. Under suitable hypotheses, we construct a map from unstable to stable operations, left-inverse to the usual map from stable to unstable operations. In the main example, where the target theory is one of the Morava K–theories, this provides a simple and explicit description of a splitting arising from the Bousfield–Kuhn functor.

DOI : 10.2140/agt.2008.8.1059
Keywords: cohomology operations, Morava K-theories

Stacey, Andrew  1   ; Whitehouse, Sarah  2

1 Institutt for Matematiske fag, NTNU, 7491 Trondheim, Norway
2 Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom 
@article{10_2140_agt_2008_8_1059,
     author = {Stacey, Andrew and Whitehouse, Sarah},
     title = {Stable and unstable operations in mod p cohomology theories},
     journal = {Algebraic and Geometric Topology},
     pages = {1059--1091},
     year = {2008},
     volume = {8},
     number = {2},
     doi = {10.2140/agt.2008.8.1059},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.1059/}
}
TY  - JOUR
AU  - Stacey, Andrew
AU  - Whitehouse, Sarah
TI  - Stable and unstable operations in mod p cohomology theories
JO  - Algebraic and Geometric Topology
PY  - 2008
SP  - 1059
EP  - 1091
VL  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.1059/
DO  - 10.2140/agt.2008.8.1059
ID  - 10_2140_agt_2008_8_1059
ER  - 
%0 Journal Article
%A Stacey, Andrew
%A Whitehouse, Sarah
%T Stable and unstable operations in mod p cohomology theories
%J Algebraic and Geometric Topology
%D 2008
%P 1059-1091
%V 8
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2008.8.1059/
%R 10.2140/agt.2008.8.1059
%F 10_2140_agt_2008_8_1059
Stacey, Andrew; Whitehouse, Sarah. Stable and unstable operations in mod p cohomology theories. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 1059-1091. doi: 10.2140/agt.2008.8.1059

[1] M Bendersky, The BP Hopf invariant, Amer. J. Math. 108 (1986) 1037

[2] J M Boardman, Stable operations in generalized cohomology, from: "Handbook of algebraic topology", North-Holland (1995) 585

[3] J M Boardman, D C Johnson, W S Wilson, Unstable operations in generalized cohomology, from: "Handbook of algebraic topology", North-Holland (1995) 687

[4] A K Bousfield, Uniqueness of infinite deloopings for $K$–theoretic spaces, Pacific J. Math. 129 (1987) 1

[5] A K Bousfield, On the telescopic homotopy theory of spaces, Trans. Amer. Math. Soc. 353 (2001) 2391

[6] T Kashiwabara, N Strickland, P Turner, The Morava $K$–theory Hopf ring for $BP$, from: "Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994)", Progr. Math. 136, Birkhäuser (1996) 209

[7] N J Kuhn, Morava $K$–theories and infinite loop spaces, from: "Algebraic topology (Arcata, CA, 1986)", Lecture Notes in Math. 1370, Springer (1989) 243

[8] N J Kuhn, Localization of André–Quillen–Goodwillie towers, and the periodic homology of infinite loopspaces, Adv. Math. 201 (2006) 318

[9] D Quillen, On the formal group laws of unoriented and complex cobordism theory, Bull. Amer. Math. Soc. 75 (1969) 1293

[10] D C Ravenel, W S Wilson, The Hopf ring for complex cobordism, J. Pure Appl. Algebra 9 (1976/77) 241

[11] C Rezk, The units of a ring spectrum and a logarithmic cohomology operation, J. Amer. Math. Soc. 19 (2006) 969

[12] W S Wilson, The Hopf ring for Morava $K$–theory, Publ. Res. Inst. Math. Sci. 20 (1984) 1025

Cité par Sources :