Brown–Peterson cohomology
- Brown–Peterson cohomology
In mathematics, Brown–Peterson cohomology is a generalized cohomology theory introduced byharvtxt|Brown|Peterson|1966, depending on a choice of prime "p". It is described in detail by harvtxt|Ravenel|2003|loc=Chapter 4.
Its spectrum is usually denoted by BP.Its coefficient ring π*(BP) is a polynomial algebra over Z("p") on generators "vn" of dimension 2("p""n" − 1) for "n" ≥ 1.Brown–Peterson cohomology BP is a summand of MU"p", which is complex cobordism MU localized at a prime "p". In fact MU"(p)" is a sum of suspensions of BP.
It is used as the initial term of the Adams-Novikov spectral sequence for calculating homotopy groups of spheres.
ee also
*List of cohomology theories#Brown–Peterson cohomology
References
*citation|id=MR|0192494|last= Brown|first= Edgar H., Jr.|last2= Peterson|first2= Franklin P. |title=A spectrum whose Zp cohomology is the algebra of reduced "p"th powers. |journal= Topology |volume= 5 |year= 1966 |pages=149--154
doi=10.1016/0040-9383(66)90015-2 .
*citation |id=MR|0253350|last= Quillen|first= Daniel |title=On the formal group laws of unoriented and complex cobordism theory|journal= Bull. Amer. Math. Soc. |volume=75 |year=1969 |pages=1293-1298
url=http://www.ams.org/bull/1969-75-06/S0002-9904-1969-12398-0/S0002-9904-1969-12398-0.pdf.
*
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