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Equivariant Gottlieb groups

Marek Golasiński, Daciberg Lima Gonçalves (2001)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska (2001)

Fundamenta Mathematicae

Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space ( B p ( G ) ) / G of the classifying space of the category associated to the G-poset p ( G ) of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor X E / ( N E . . . N E ) defined over the poset ( s d p ( G ) ) / G , where sd is the barycentric subdivision. We also...

Injective models of G -disconnected simplicial sets

Marek Golasiński (1997)

Annales de l'institut Fourier

We generalize the results by G.V. Triantafillou and B. Fine on G -disconnected simplicial sets. An existence of an injective minimal model for a complete 𝕀 -algebra is presented, for any E I -category 𝕀 . We then make use of the E I -category 𝒪 ( G , X ) associated with a G -simplicial set X to apply these results to the category of G -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent G -simplicial set by means of its injective minimal model.

On G -disconnected injective models

Marek Golasiński (2003)

Annales de l’institut Fourier

Let G be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the G -connected case is incorrect because of an error concerning algebraic properties. In the G -disconnected case the orbit category 𝒪 ( G ) was originally replaced by the category 𝒪 ( G , X ) with one object for each component of each fixed point simplicial subsets X H of a G -simplicial set X , for all subgroups H G . We redefine the equivariant minimality and redevelop some results on the rational homotopy...

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