Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2021

    starting something, for the moment mainly to record the other result of Brown & Szczarba (dg-algebraic rational homotopy theory for general connected spaces)

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 27th 2021

    added pointer to:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 25th 2021

    added pointer to the recent:

    • Sergei O. Ivanov, Section 12 of: An overview of rationalization theories of non-simply connected spaces and non-nilpotent groups (arXiv:2111.10694)

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2021

    added pointer to:

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2021

    finally had a closer look at Gómez-Tato, Halperin & Tanré 2000, but I don’t see clearly yet on the key point:

    As opposed to Brown & Szczarba 1995 these authors develop a theory that does not have explicit π 1\pi_1-actions on dg-algebras, but instead is formulated in terms of dg-algebra valued functors on the category of elements of a simplicial set modelling Bπ 1B \pi_1. On the other hand, the examples offered towards the end (Examples. 6.6 - 6.8) suddenly speak of π 1\pi_1-actions via dg-algebra automorphisms, but seemingly not about those functors on categories of elements that occupy the bulk of the article.

    I am getting the impression that the connective tissue between theory and examples is meant to be Prop. 3.17, which claims, it seems (without further proof or argument), that from the previous Theorem 3.12 one dg-algebra automorphism may be extracted. Currently I have trouble even parsing the ingredients appearing in Prop. 3.17. E.g. the “ϕ\phi” here seems to be different from the ϕ\phi on the previous pages and throughout.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 16th 2022
    • (edited Jul 16th 2022)

    added pointer to

    for further discussion of fiberwise rational homotopy theory.

    diff, v10, current