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  • 1.
    Baker, Andrew
    et al.
    Univ Glasgow, Sch Math & Stat, Glasgow, Lanark, Scotland. Kungliga Tekn Högskolan, Inst Matemat, Stockholm, Sweden..
    Bauer, Tilman
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    The realizability of some finite-length modules over the Steenrod algebra by spaces2020Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 20, nr 4, s. 2129-2143Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Joker is an important finite cyclic module over the mod-2 Steenrod algebra A. We show that the Joker, its first two iterated Steenrod doubles, and their linear duals are realizable by spaces of as low a dimension as the instability condition of modules over the Steenrod algebra permits. This continues and concludes prior work by the first author and yields a complete characterization of which versions of Jokers are realizable by spaces or spectra and which are not. The constructions involve sporadic phenomena in homotopy theory (2-compact groups, topological modular forms) and may be of independent interest.

  • 2.
    Chacholski, Wojciech
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Scherer, Jerome
    Representations of spaces2008Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 8, nr 1, s. 245-278Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be able to construct resolutions. We prove that the homotopy category of any monoidal model category is always a central algebra over the homotopy category of Spaces.

  • 3.
    Moi, Kristian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Equivariant loops on classifying spaces2020Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 20, nr 5, s. 2511-2552Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We compute the homology of the space of equivariant loops on the classifying space of a simplicial monoid M with anti-involution, provided pi(0)(M) is central in the homology ring of M. The proof is similar to McDuff and Segal's proof of the group completion theorem. Then we give an analogous computation of the homology of the C-2 -fixed points of a Gamma-space-type delooping of an additive category with duality with respect to the sign circle. As an application we show that this fixed-point space is sometimes group complete, but in general not.

  • 4.
    Ziegenhagen, Stephanie
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    En-cohomology with coefficients as functor cohomology2016Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 16, nr 5, s. 2981-3004Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Building on work of Livernet and Richter, we prove that En -homology and En - cohomology of a commutative algebra with coefficients in a symmetric bimodule can be interpreted as functor homology and cohomology. Furthermore, we show that the associated Yoneda algebra is trivial.

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