Models For The Maclaurin Tower Of A Simplicial Functor Via A Derived Yoneda Embedding

Details Models For The Maclaurin Tower Of A Simplicial Functor Via A Derived Yoneda Embedding Models For The Maclaurin Tower Of A Simplicial Functor Via A Derived Yoneda Embedding

2009-12-18

arxiv.org/abs/0912.3567v1

Mathematics

Algebraic Topology

14 pages

Scientific paper

We prove that the Goodwillie tower of a weak equivalence preserving functor from spaces to spectra can be expressed in terms of the tower for stable mapping spaces. Our proof is motivated by interpreting the functors P_n and D_n as pseudo-differential operators which suggests certain `integral' presentations based on a derived Yoneda embedding. These models allow one to extend computational tools available for the tower of stable mapping spaces. As an application we give a classical expression for the derivative over the basepoint.

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