Homotopy theory and classifying spaces
نویسنده
چکیده
What is a homotopy theory T? – Examples of homotopy theories (Tpair presentation) – The homotopy category Ho(T) – Examples of homotopy categories – Model category: (C, E) with extras – Examples of model categories (C, E) – Dividends from a model category structure on (C, E) – Equivalences between homotopy theories – T(C, E) ∼ T(C′, E ′) for model categories – Examples of equivalences between homotopy theories
منابع مشابه
Classifying Spaces and Homology Decompositions
Suppose that G is a finite group. We look at the problem of expressing the classifying space BG, up to mod p cohomology, as a homotopy colimit of classifying spaces of smaller groups. A number of interesting tools come into play, such as simplicial sets and spaces, nerves of categories, equivariant homotopy theory, and the transfer.
متن کاملHomotopy Theory of Lie groups and their Classifying Spaces
1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps be...
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 کاملHomotopy Theory of Classifying Spaces of Compact Lie Groups
The basic problem of homotopy theory is to classify spaces and maps between spaces, up to homotopy, by means of invariants like cohomology. In the last decade some striking progress has been made with this problem when the spaces involved are classifying spaces of compact Lie groups. For example, it has been shown, for G connected and simple, that if two self maps of BG agree in rational cohomo...
متن کاملCellularization of Classifying Spaces and Fusion Properties of Finite Groups
One way to understand the mod p homotopy theory of classifying spaces of finite groups is to compute their BZ/p-cellularization. In the easiest cases this is a classifying space of a finite group (always a finite p-group). If not, we show that it has infinitely many non-trivial homotopy groups. Moreover they are either p-torsion free or else infinitely many of them contain p-torsion. By means o...
متن کامل