Goodwillie calculus – approximation of homotopy theories by stable homotopy theories
In the context of Goodwillie calculus the Taylor tower of an (∞,1)-functor $F$ to a Goodwillie-differentiable (∞,1)-category is its stagewise approximation by n-excisive (∞,1)-functors $P_n F$ (its n-excisive projections)
which is analogous to the approximation of a smooth function by its Taylor series.
If this tower converges to $F$, then $F$ is analogous to an analytic function and is called an analytic (∞,1)-functor.
The spectral sequence induced by the filtration given by the Goodwillie-Taylor tower is the Goodwillie spectral sequence.
convergence for $\rho$-analytic (∞,1)-functors on $\rho$-connective objects (…) (Goodwillie 03, theorem 1.13, see also Munson-Volic 15, theorem 10.1.51 and section 10.2.4)
Under some conditions, the Goodwillie-Taylor tower of mapping spaces into sufficiently high suspensions is a direct sum of suspension spectra of configuration spaces. This stable splitting of mapping spaces is originally due to (Snaith 74, Bödigheimer 87) and was understood as a Goodwillie-Taylor tower in Arone 99, see also Ching 05.
The concept originates in
Review includes
See also
The stable splitting of mapping spaces is originally due to
Review and generalization is due to
Further generalization and interpretation in terms of the Goodwillie-Taylor tower of mapping spaces is due to
Greg Arone, A generalization of Snaith-type filtration, Transactions of the American Mathematical Society 351.3 (1999): 1123-1150. (pdf)
Michael Ching, Calculus of Functors and Configuration Spaces, Conference on Pure and Applied Topology Isle of Skye, Scotland, 21-25 June, 2005 (pdf)
Last revised on November 2, 2018 at 08:33:27. See the history of this page for a list of all contributions to it.