Homotopy category

We define and study sl2 -categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´’s abelian defect group conjecture for symmetric groups. e We give similar results for general linear groups over finite fields. ...

55p dontetvui 17-01-2013 51 8   Download

The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

28p noel_noel 17-01-2013 50 6   Download

Characteristic cohomology classes, defined in modulo 2 coefficients by Stiefel [26] and Whitney [28] and with integral coefficients by Pontrjagin [24], make up the primary source of first-order invariants of smooth manifolds. When their utility was first recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.

25p tuanloccuoi 04-01-2013 58 6   Download