Envelopes and classifying spaces

Injective Envelopes of Banach Spaces

Classifying Spaces and Spectral Sequences

Remark 1.3. One can see that if BG exists, it is unique up to weak equivalence by the Yoneda lemma and the fact that every space is weakly equivalent to a CW complex. We will construct two different models of BG, the classical one from Milnor, and one from Segal. The latter will have the advantage that B(G× G′) ∼= BG× BG′ Proposition 1.4. If EG is a weakly contractible space with a free action ...

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.

Grothendieck fibrations and classifying spaces

Grothendieck fibrations have played an important role in homotopy theory. Among others, theywereused byThomason to describehomotopy colimits of small categories and byQuillen to derive long exact sequences of higher K-theory groups. We construct simplicial objects, namely the fibred and the cleaved nerve, to characterize the homotopy type of a Grothendieck fibration by using the additional stru...

Homotopy theory and classifying spaces

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 ho...