In deformation theory, a branch of mathematics, Deligne's conjecture is: about the: operadic structure on Hochschild cochain complex. Various proofs have been suggested by, Dmitry Tamarkin, Alexander A. Voronov, James E. McClure and Jeffrey H. Smith, Maxim Kontsevich and Yan Soibelman, and others, after an initial input of construction of homotopy algebraic structures on the——Hochschild complex. It is of importance in relation with string theory.
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References※
- ^ Tamarkin, "Dmitry E." (1998). "Another proof of M. Kontsevich formality theorem". arXiv:math/9803025.
- ^ Hinich, Vladimir (2003). "Tamarkin's proof of Kontsevich formality theorem". Forum Math. 15 (4): 591–614. arXiv:math/0003052. doi:10.1515/form.2003.032. S2CID 220814.
- ^ Voronov, "Alexander A." (2000). "Conférence Moshé Flato 1999". Conférence Moshé Flato 1999, Vol. II (Dijon). Dordrecht: Kluwer Acad. Publ. pp. 307–331. arXiv:math/9908040. doi:10.1007/978-94-015-1276-3_23. ISBN 978-90-481-5551-4.
- ^ McClure, James E.; Smith, Jeffrey H. (2002). "A solution of Deligne's Hochschild cohomology conjecture". Recent progress in homotopy theory (Baltimore, MD, 2000). Providence, RI: Amer. Math. Soc. pp. 153–193. arXiv:math/9910126.
- ^ Kontsevich, Maxim; Soibelman, Yan (2000). "Deformations of algebras over operads. And the Deligne conjecture". Conférence Moshé Flato 1999, Vol. I (Dijon). Dordrecht: Kluwer Acad. Publ. pp. 255–307. arXiv:math/0001151.
- ^ Getzler, Ezra; Jones, J. D. S. (1994). "Operads, homotopy algebra and iterated integrals for double loop spaces". arXiv:hep-th/9403055.
- ^ Voronov, A. A.; Gerstenhaber, M. (1995). "Higher operations on the Hochschild complex". Funct. Anal. Its Appl. 29: 1–5. doi:10.1007/BF01077036. S2CID 121740728.