# Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

Fundamenta Mathematicae (1999)

- Volume: 160, Issue: 1, page 81-93
- ISSN: 0016-2736

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topSlack, Michael. "Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology." Fundamenta Mathematicae 160.1 (1999): 81-93. <http://eudml.org/doc/212382>.

@article{Slack1999,

abstract = {A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem is given as a sample computation.},

author = {Slack, Michael},

journal = {Fundamenta Mathematicae},

keywords = {Brown-Peterson spectrum; Hopf invariant one theorem},

language = {eng},

number = {1},

pages = {81-93},

title = {Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology},

url = {http://eudml.org/doc/212382},

volume = {160},

year = {1999},

}

TY - JOUR

AU - Slack, Michael

TI - Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

JO - Fundamenta Mathematicae

PY - 1999

VL - 160

IS - 1

SP - 81

EP - 93

AB - A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem is given as a sample computation.

LA - eng

KW - Brown-Peterson spectrum; Hopf invariant one theorem

UR - http://eudml.org/doc/212382

ER -

## References

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- [6] R. Kane, Brown-Peterson operations and Steenrod modules, Quart. J. Math. Oxford 30 (1979), 455-467. Zbl0461.55012
- [7] P. S. Landweber, Homological properties of comodules over $M{U}_{*}MU$ and BP${}_{*}$BP, Amer. J. Math. 98 (1976), 591-610.
- [8] A. L. Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. 42 (1962). Zbl0131.38101
- [9] J. W. Milnor, The Steenrod algebra and its dual, Ann. of Math. 67 (1958), 150-171. Zbl0080.38003
- [10] D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986.

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