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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Functional equations and their related operads


Author: Vahagn Minasian
Journal: Trans. Amer. Math. Soc. 357 (2005), 4413-4443
MSC (2000): Primary 55U15; Secondary 18D50, 55P99
Published electronically: June 9, 2005
MathSciNet review: 2156716
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Abstract: 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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Additional Information

Vahagn Minasian
Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912-1917
Email: minasian@math.brown.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03974-7
PII: S 0002-9947(05)03974-7
Keywords: Little $n$-cubes operads, Goodwillie calculus, functional equations
Received by editor(s): June 16, 2003
Published electronically: June 9, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.