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 ,[ 1] [ 2] Alexander A. Voronov ,[ 3] James E. McClure and Jeffrey H. Smith ,[ 4] Maxim Kontsevich and Yan Soibelman ,[ 5] and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex.[ 6] [ 7] It is of importance in relation with string theory .
See also
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 .
Further reading