Homotopical Linking and Morse Index estimates in Min-max Theroems.
Summary: All algebraic objects in this note will be considered over a fixed field of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over . 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,...
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all -Galois extensions up to homotopy equivalence in the case when is a Drinfeld-Jimbo quantum group.
Let denote the configuration space of pairwise-disjoint -tuples of points in . In this short note the author describes a cellular structure for when . 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 is well-understood. This allows an identification of the location of the cells of in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...
We employ the notion of the universal differential calculus to propose yet another approach to the Hopf-type cohomology of Hopf algebras.