2013/11/19 by Matan Prasma, Prasma, Matan
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT
paper · pdf · doi:10.48550/arxiv.1311.4749
Final version. To appear in TAC
arxiv created 2015/09/16 · arxiv updated 2015/09/18
We define a model category structure on a slice category of simplicial spaces, called the "Segal group action" structure whose fibrant-cofibrant objects may be viewed as representing spaces X with a coherent action of a given Segal group (i.e. a group-like, reduced Segal space). We show that this model structure is Quillen equivalent to the projective model structure on G-spaces, S^\mathbbBG, where G is a simplicial group represented by this Segal group. Since Segal group actions are invariant under weak monoidal endofunctors of spaces they enable to construct, for an arbitrary G-space X, an "equivariant Postnikov tower" which in degree n has PnX viewed as a space with a coherent action of (the Segal group corresponding to) PnG.