Groupe de Travail: On the chain rule in Goodwillie Calculus
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organized by Georg Biedermann and Eric Hoffbeck
to understand aspects of the work by Arone and Ching on the chain rule in Goodwillie's calculus of homotopy functors
- 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,
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- 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
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- 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
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- 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
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- 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
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- Talk 4: G. Biedermann (17.3.2016)
- Sections 3-6
- Trees, bar construction for operads, its cooperad structure, Spanier-Whitehead duality
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- Talk 5: G. Biedermann (31.3.2016)
- Sections 7/8
- generalized trees, generalized bar constructions, the operad structure of the derivatives of the identity
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- Koszul Duality
- Talk 6: Bruno Vallette/Daniel Robert-Nicoud (21.4.2016)
- An introduction to Koszul duality
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- 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
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- to be continued ...
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