# Some Technical Aspects of Factorization Algebras on Manifolds

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## Abstract

We describe the basic ideas of factorization algebras on manifolds and topological chiral homology, with emphasis on their gluing properties.

## Keywords

Factorization algebra Topological chiral homology \(E_n\)-algebra Homotopical algebra## Notes

### Acknowledgements

The author is grateful to the anonymous referee for the fair criticism and helpful suggestions.

## References

- 1.Anderson, D.W.: Chain functors and homology theories. In: Symposium Algebraic Topology. Lecture Notes in Mathematics, vol. 249, pp. 1–12 (1971)Google Scholar
- 2.Ayala, D., Francis, J.: Factorization homology of topological manifolds. J. Topol.
**8**(4), 1045–1084 (2015)MathSciNetCrossRefGoogle Scholar - 3.Beilinson, A., Drinfeld, V.: Chiral Algebras. American Mathematical Society Colloquium Publications. vol. 51, vi\(+\)375 pp. American Mathematical Society, Providence, RI (2004). ISBN: 0-8218-3528-9Google Scholar
- 4.Boardman, J.M., Vogt, R.M.: Homotopy invariant algebraic structures on topological spaces. Lecture Notes in Mathematics, vol. 347. Springer, Berlin-New York (1973)CrossRefGoogle Scholar
- 5.Calaque, D.: Around Hochschild (co)homology. Habilitation thesis, Université Claude Bernard Lyon 1 (2013)Google Scholar
- 6.Costello, K., Gwilliam, O.: Factorization algebras in quantum field theory. Draft available at http://www.math.northwestern.edu/~costello/
- 7.Dunn, G.: Tensor product of operads and iterated loop spaces. J. Pure Appl. Algebra
**50**(3), 237–258 (1988)MathSciNetCrossRefGoogle Scholar - 8.Ginot, G.: Notes on factorization algebras, factorization homology and applications. Calaque, D. et al. (ed.) Mathematical aspects of quantum field theories. Springer. Mathematical Physics Studies, pp. 429–552 (2015)Google Scholar
- 9.Ginot, G., Tradler, T., Zeinalian, M.: Higher Hochschild homology, topological chiral homology and factorization algebras. Commun. Math. Phys.
**326**(3), 635–686 (2014)MathSciNetCrossRefGoogle Scholar - 10.Kontsevich, M.: Operads and motives in deformation quantization. Mosh Flato (1937–1998). Lett. Math. Phys.
**48**(1), 35–72 (1999)Google Scholar - 11.Lurie, J.: Higher Algebra (2017). http://www.math.harvard.edu/~lurie/
- 12.Matsuoka, T.: Descent properties of the topological chiral homology. Münster J. Math.
**10**, 83–118 (2017). Mathematical Reviews MR3624103. Available via https://www.uni-muenster.de/FB10/mjm/vol10.html - 13.Pirashvili, T.: Hodge decomposition for higher order Hochschild homology. Ann. Sci. Éc. Norm. Supér. (4)
**33**(2), 151–179 (2000)MathSciNetCrossRefGoogle Scholar

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