## Functional equations and their related operads

HTML articles powered by AMS MathViewer

- by Vahagn Minasian PDF
- Trans. Amer. Math. Soc.
**357**(2005), 4413-4443 Request permission

## 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.## References

- Glen E. Bredon,
*Topology and geometry*, Graduate Texts in Mathematics, vol. 139, Springer-Verlag, New York, 1993. MR**1224675**, DOI 10.1007/978-1-4757-6848-0 - Frederick R. Cohen, Thomas J. Lada, and J. Peter May,
*The homology of iterated loop spaces*, Lecture Notes in Mathematics, Vol. 533, Springer-Verlag, Berlin-New York, 1976. MR**0436146**, DOI 10.1007/BFb0080464 - A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May,
*Rings, modules, and algebras in stable homotopy theory*, Mathematical Surveys and Monographs, vol. 47, American Mathematical Society, Providence, RI, 1997. With an appendix by M. Cole. MR**1417719**, DOI 10.1090/surv/047 - Edward Fadell and Lee Neuwirth,
*Configuration spaces*, Math. Scand.**10**(1962), 111–118. MR**141126**, DOI 10.7146/math.scand.a-10517 - E.Getzler and J.D.S.Jones.
*Operads, Homotopy Algebra, and Iterated Integrals for Double Loop Spaces.*Preprint. 1993 - Thomas G. Goodwillie,
*Calculus. I. The first derivative of pseudoisotopy theory*, $K$-Theory**4**(1990), no. 1, 1–27. MR**1076523**, DOI 10.1007/BF00534191 - Thomas G. Goodwillie,
*Calculus. II. Analytic functors*, $K$-Theory**5**(1991/92), no. 4, 295–332. MR**1162445**, DOI 10.1007/BF00535644 - Thomas G. Goodwillie,
*Calculus. III. Taylor series*, Geom. Topol.**7**(2003), 645–711. MR**2026544**, DOI 10.2140/gt.2003.7.645 - B. Johnson and R. McCarthy,
*Deriving calculus with cotriples*, Trans. Amer. Math. Soc.**356**(2004), no. 2, 757–803. MR**2022719**, DOI 10.1090/S0002-9947-03-03318-X - Igor Kříž and J. P. May,
*Operads, algebras, modules and motives*, Astérisque**233**(1995), iv+145pp (English, with English and French summaries). MR**1361938** - R.McCarthy and V.Minasian.
*On Triples, Operads and Generalized Homogeneous Functors*. Preprint, 2004 - John W. Milnor and John C. Moore,
*On the structure of Hopf algebras*, Ann. of Math. (2)**81**(1965), 211–264. MR**174052**, DOI 10.2307/1970615 - Vahagn Minasian,
*André-Quillen spectral sequence for $THH$*, Topology Appl.**129**(2003), no. 3, 273–280. MR**1962984**, DOI 10.1016/S0166-8641(02)00184-0 - Daniel Quillen,
*On the (co-) homology of commutative rings*, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 65–87. MR**0257068** - Alan Robinson,
*Gamma homology, Lie representations and $E_\infty$ multiplications*, Invent. Math.**152**(2003), no. 2, 331–348. MR**1974890**, DOI 10.1007/s00222-002-0272-5 - Charles A. Weibel,
*An introduction to homological algebra*, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, Cambridge, 1994. MR**1269324**, DOI 10.1017/CBO9781139644136

## Additional Information

**Vahagn Minasian**- Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912-1917
- Email: minasian@math.brown.edu
- Received by editor(s): June 16, 2003
- Published electronically: June 9, 2005
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**357**(2005), 4413-4443 - MSC (2000): Primary 55U15; Secondary 18D50, 55P99
- DOI: https://doi.org/10.1090/S0002-9947-05-03974-7
- MathSciNet review: 2156716