## Brown-Peterson Homology: An Introduction and Sampler, Issue 48This book is primarily directed to graduate students interested in the field and to algebraic topologists who wish to learn something about BP. Beginning with the geometric background of complex bordism, the author goes on to a discussion of formal groups and an introduction to BP-homology. He then presents his view of the major developments in the field in the last decade (the calculation of the homology of Eilenberg-MacLane spaces in this section may be useful in teaching advanced algebraic topology courses). The book concludes with a section on unstable operations with comments on where applications may come from in the future. |

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### Contents

3 | |

Section 2 Formal groups | 12 |

Section 3 BrownPeterson homology | 14 |

Part II A Sampler | 23 |

Section 5 Association homology theories | 34 |

Section 6 Moravas little structure theorem and the ConnerFloyd conjecture | 38 |

Section 7 Hopf rings the bar spectral sequence and KnK | 44 |

Section 8 HK and the Steenrod algebra | 51 |

Section 9 Two formal groups and BPBP | 56 |

Section 10 Chans proof of no torsion in HBP | 59 |

Part III Something New | 61 |

### Common terms and phrases

abelian group abelian group object Apply exp associated homology theories Atiyah-Hirzebruch spectral sequence bar spectral sequence Bockstein BP operations BP*BP BP^BP BP+ module BP+BP BP+X BPJI BPJIn Brown-Peterson homology BU(n Chan's proof coalgebras coefficients cofibration cohomology suspension comodule complex bordism complex cobordism compute Conner-Floyd conjecture coproduct define degree diagram dual Eilenberg-MacLane spaces elements exact sequence example extension problems exterior algebra finite formal group law formal group sum formula geometry give grbimod H2BP+ HlBPJ(p homology theories Hopf algebra idempotent induction isomorphism lectures LEMMA manifolds Math module structure Morava Morava structure theorem MU(n MU*CP MU*MU MU+MU MU+X obtain pairing PBP*BPn polynomial algebra power series prime primitively QUILLEN Ravenel RAVENEL-WILSON result ring map spectral sequence collapses spectrum stable homotopy Steenrod algebra tensor product tion topological unstable E*E module unstable module unstable operations unstable structure vn_l

### Popular passages

Page 83 - NA Baas, On bordism theory of manifolds with singularities.