## Algebraic Topology: The Abel Symposium 2007Nils Baas, Eric Friedlander, Björn Jahren, Paul Arne Østvær The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new. |

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### Contents

1 | |

String Topology in Dimensions Two and Three | 32 |

Floer Homotopy Theory Realizing Chain Complexes by Module Spectra and Manifolds with Corners | 39 |

Relative Chern Characters for Nilpotent Ideals | 60 |

Algebraic Differential Characters of FlatConnections with Nilpotent Residues | 83 |

Norm Varieties and the Chain Lemma After Markus Rost | 95 |

On the Whitehead Spectrum of the Circle | 131 |

Cocycle Categories | 185 |

A Survey of Elliptic Cohomology | 219 |

On Voevodskys Algebraic KTheory Spectrum | 279 |

Chern Character Loop Spaces and Derived Algebraic Geometry | 331 |

Voevodskys Lectures on Motivic Cohomology 20002001 | 355 |

### Other editions - View all

Algebraic Topology: The Abel Symposium 2007 Nils Baas,Eric Friedlander,Björn Jahren,Paul Arne Østvær No preview available - 2009 |

### Common terms and phrases

½-ring 2-group ¾-category Ã-theory abelian group adjoint afﬁne algebraic geometry Àº canonical Chain Lemma Chern character classifying space cocycle cofibrant coﬁbrations cohomology theory colimit commutative ring composition construction Corollary CP½ cyclic deﬁned Deﬁnition denote derived scheme diagram Ë½ element elliptic cohomology elliptic curve equivariant exact sequence ﬁbration ﬁeld ﬁnite ﬁrst ﬂat Floer follows formal group functor group G groupoid hence homology homomorphism homotopy category homotopy equivalence homotopy groups induced integers isomorphism line bundle manifold Math model structure moduli spaces monoidal morphism multiplicative nilpotent Nisnevich norm º½ object ºÍ oriented pointed motivic space pointed simplicial presheaf Proof Proposition prove Quillen sheaf simplicial presheaves simplicial sets simplicial sheaves smooth Spec spectra spectral sequence spectrum stable stack Suppose symmetric monoidal Theorem topological group torsors trivial vector bundles weak equivalence Ý Ý zero