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Homotopy algebras via resolutions of operads

Markl, Martin (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: All algebraic objects in this note will be considered over a fixed field k of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over k . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...

Homotopy theory of Hopf Galois extensions

Christian Kassel, Hans-Jürgen Schneider (2005)

Annales de l'institut Fourier

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H -Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.

Homotopy type of Euclidean configuration spaces

Salvatore, Paolo (2001)

Proceedings of the 20th Winter School "Geometry and Physics"

Let F ( n , k ) denote the configuration space of pairwise-disjoint k -tuples of points in n . In this short note the author describes a cellular structure for F ( n , k ) when n 3 . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of F ( n , k ) is well-understood. This allows an identification of the location of the cells of F ( n , k ) in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...

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