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Invariants homotopiques attachés aux fibrés symplectiques

Pierre Dazord (1979)

Annales de l'institut Fourier

On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne 2 q -orientée dans R n R n * : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré q -symplectique, c’est-à-dire dont le groupe structural est le revêtement à q feuillets de S p ( n ) . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...

K ( π , 1 ) conjecture for Artin groups

Luis Paris (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The purpose of this paper is to put together a large amount of results on the K ( π , 1 ) conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as...

Karoubi’s relative Chern character and Beilinson’s regulator

Georg Tamme (2012)

Annales scientifiques de l'École Normale Supérieure

We construct a variant of Karoubi’s relative Chern character for smooth varieties over 𝐂 and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.

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