Groupe de Travail: On the chain rule in Goodwillie Calculus

    organized by Georg Biedermann and Eric Hoffbeck

    The Goal:

    to understand aspects of the work by Arone and Ching on the chain rule in Goodwillie's calculus of homotopy functors

    Main References:

    • Goodwillie "Calculus III: Taylor series", G and T, vol 7, 645--711 (electronic), 2003.
    • Ching "A chain rule for Goodwillie derivatives of functors from spectra to spectra", Trans. Amer. Math. Soc., 362(1):399--426, 2010.
    • Ching "Bar constructions for topological operads and the Goodwillie derivatives of the identity", G and T, vol. 9, 833--933 (electronic), 2005
    • Arone/Ching "Operads and chain rules for the calculus of functors", Astérisque, vol. 338, vi+158pp, Soc. Math. France, Paris, 2011,

    Other useful References:

    • Kuhn "Goodwillie towers and chromatic homotopy: an overview", Proceedings of the Nishida Fest (Kinosaki 2003), Geom. Topol. Monogr., vol. 10, pp 245--279, 2007
    • Goodwillie "The differential calculus of homotopy functors", Proceedings of the International Congress of Mathematicians, Vol.\ I, II (Kyoto, 1990), pp. 621--630, Math. Soc. Japan, Tokyo, 1991
    • Goodwillie "Calculus. I. The first derivative of pseudoisotopy theory", K-Theory, vol. 4, 1990, no. 1, pp 1--27,
    • Goodwillie "Calculus. II. Analytic functors", K-Theory, vol. 5, 1991/92, no. 4, pp 295--332
    • Arone/Mahowald "The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres", Invent. Math., vol. 135, 1999, no. 3, pp 743--788
    • Arone/Dwyer "Partition complexes, Tits buildings and symmetric products", Proc. London Math. Soc. (3), vol. 82, 2001, no. 1, pp 229--256

    Outline:

    • Goodwillie "Calculus III: The Taylor tower"
      • Talk 1: E. Hoffbeck, 28.1.2016
      • A summary of Sections 1-5 in Goodwillie's paper
      • Introduction to Goodwillie Calculus
    • Ching "A chain rule for Goodwillie derivatives of functors from spectra to spectra"
      • Talk 2: C. Ausoni, 11.2.2016
      • Section 1
      • Derivatives and the chain rule for endofunctors of spectra
    • Ching "Bar constructions for topological operads and the Goodwillie derivatives of the identity"
      • Talk 3: M. Palmer (1.3.2016)
      • Sections 1, 2
      • Symmetric monoidal V-categories, (co-)operads, (co-)modules, (co-)algebras
      • Talk 4: G. Biedermann (17.3.2016)
      • Sections 3-6
      • Trees, bar construction for operads, its cooperad structure, Spanier-Whitehead duality
      • Talk 5: G. Biedermann (31.3.2016)
      • Sections 7/8
      • generalized trees, generalized bar constructions, the operad structure of the derivatives of the identity
    • Koszul Duality
      • Talk 6: Bruno Vallette/Daniel Robert-Nicoud (21.4.2016)
      • An introduction to Koszul duality
    • Ching "Bar constructions for topological operads and the Goodwillie derivatives of the identity"
      • Talk 7: Eric Hoffbeck (21.4.2016)
      • Section 9
      • Koszul duality and the homology of the derivatives of the identity
    • to be continued ...