Functional Equations and Their Related Operads

Details Functional Equations and Their Related Operads Functional Equations and Their Related Operads

2003-06-16

arxiv.org/abs/math/0306241v1

Mathematics

Algebraic Topology

35 pages

Scientific paper

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through objects enriched over the homology of little $n$-cubes operads and discuss the relationship between functors defined via functional equations and operads. In addition, we compute the differentials of the forgetful functor from the category of $n$-Poisson algebras in terms of the homology of configuration spaces.

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