Rational Homotopy Groups of Generalised Symmetric Spaces
نویسنده
چکیده
We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In particular, this gives explicit formulas for the rational homotopy groups of all classical compact symmetric spaces.
منابع مشابه
Elliptic spaces with the rational homotopy type of spheres
The Milnor-Moore theorem shows that the Q-elliptic spaces are precisely those spaces which have the rational homotopy type of finite, 1-connected CW complexes and have finite total rational homotopy rank. This class of spaces is important because of the dichotomy theorem (the subject of the book [8]) which states that a finite, 1-connected complex either has finite total rational homotopy rank ...
متن کاملAndré–Quillen cohomology and rational homotopy of function spaces
We develop a simple theory of André–Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework. © 2004 Elsevier Inc. All rights reserved.
متن کاملA ug 1 99 8 Spaces of maps into classifying spaces for equivariant crossed complexes , II : The general topological group case
Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for cross...
متن کاملOn Formality of Generalised Symmetric Spaces
We prove that all generalised symmetric spaces of compact simple Lie groups are formal in the sense of Sullivan. Nevertheless, many of them, including all the non-symmetric flag manifolds, do not admit Riemannian metrics for which all products of harmonic forms are harmonic.
متن کاملar X iv : m at h / 00 10 12 6 v 1 [ m at h . A T ] 1 2 O ct 2 00 0 RATIONAL OBSTRUCTION THEORY AND RATIONAL HOMOTOPY SETS
We develop an obstruction theory for homotopy of homomorphisms f, g : M → N between minimal differential graded algebras. We assume that M = ΛV has an obstruction decomposition given by V = V0⊕V1 and that f and g are homotopic on ΛV0. An obstruction is then obtained as a vector space homomorphism V1 → H(N ). We investigate the relationship between the condition that f and g are homotopic and th...
متن کامل