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Original Articles

Cosimplicial DGLAs in Deformation Theory

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Pages 2243-2260 | Received 28 May 2008, Published online: 15 Jun 2012

REFERENCES

  • Bousfield , A. K. , Kan , A. M. ( 1972 ). Homotopy limits, completions and localizations. Lecture Notes in Mathematics 304. Springer-Verlag .
  • Cheng , X. Z. , Getzler , E. ( 2008 ). Homotopy commutative algebraic structures . J. Pure Appl. Alg. 212 : 2535 – 2542 .
  • Dupont , J. L. ( 1976 ). Simplicial de Rham cohomology and characteristic classes of flat bundles . Topology 15 : 233 – 245 .
  • Dupont , J. L. ( 1978 ). Curvature and characteristic classes. Lecture Notes in Mathematics 640. Springer-Verlag .
  • Fiorenza , D. , Manetti , M. ( 2007 ). L ∞-structures on mapping cones . Algebra & Number Theory 1 : 301 – 330 .
  • Fukaya , K. ( 2003 ). Deformation Theory, Homological Algebra and Mirror Symmetry. Geometry and physics of branes (Como, 2001), Ser. High Energy Phys. Cosmol. Gravit., IOP Bristol 121-209. Electronic version available at http://www.math.kyoto-u.ac.jp/%7Efukaya/fukaya.html. Accessed April 30, 2012 .
  • Getzler , E. ( 2009 ). Lie theory for nilpotent L ∞-algebras . Ann. of Math. 170 ( 1 ): 271 – 301 .
  • Getzler , E. ( 2007 ). Lectures given at Institut Henri Poincaré. March 2007, and Fields Institute, May .
  • Goerss , P. G. , Jardine , J. F. ( 1999 ). Simplicial Homotopy Theory. Progress in Mathematics Vol. 174. Birkhäuser Basel-Boston-Berlin .
  • Goldman , W. M. , Millson , J. J. ( 1990 ). The homotopy invariance of the Kuranishi space . Illinois J. Math. Math. 34 : 337 – 367 .
  • Hinich , V. ( 1997 ). Descent of Deligne groupoids . Internat. Math. Res. Notices 5 : 223 – 239 .
  • Hinich , V. ( 2001 ). DG coalgebras as formal stacks . J. Pure Appl. Algebra 162 : 209 – 250 .
  • Hinich , V. ( 2005 ). Deformations of sheaves of algebras . Advances in Mathematics 195 : 102 – 164 .
  • Hinich , V. , Schechtman , V. ( 1997 ). Deformation theory and Lie algebra homology . I. Algebra Colloq. 4 ( 2 ): 213 – 240 .
  • Hinich , V. , Schechtman , V. ( 1997 ). Deformation theory and Lie algebra homology. II . Algebra Colloq. 4 ( 3 ): 291 – 316 .
  • Hirzebruch , F. ( 1978 ). Topological Methods in Algebraic Geometry . Classics in Mathematics , Berlin–Heidelberg–New York : Springer-Verlag .
  • Huebschmann , J. , Kadeishvili , T. ( 1991 ). Small models for chain algebras . Math. Z. 207 : 245 – 280 .
  • Iacono , D. ( 2006 ). Differential Graded Lie Algebras and Deformations of Holomorphic Maps. Thesis, Università degli Studi di Roma “La Sapienza,” Rome, Italy .
  • Lurie , J. Moduli Problems for Ring Spectra. http://www.math.harvard.edu/[ltilde]urie/papers/ moduli.pdf. Accessed April 30, 2012.
  • Kadeishvili , T. V. ( 1982 ). The algebraic structure in the cohomology of A(∞)-algebras . Soobshch. Akad. Nauk Gruzin. SSR 108 : 249 – 252 .
  • Kontsevich , M. ( 2003 ). Deformation quantization of Poisson manifolds . I. Letters in Mathematical Physics 66 : 157 – 216 .
  • Kontsevich , M. , Soibelman , Y. ( 2000 ). Deformations of algebras over operads and Deligne's conjecture . In : Dito, G., Sternheimer, D., eds. Conférence Moshé Flato 1999, Vol. I (Dijon 1999). Dordrecht: Kluwer Acad. Publ., pp. 255–307 .
  • Kontsevich, M., Soibelman, Y. (2001). Homological mirror symmetry and torus fibrations. In: Fukaya, K., et al., eds. Symplectic Geometry and Mirror Symmetry. Proceedings of the 4th KIAS Annual International Conference, Seoul, South Korea, August 14–18, 2000. Singapore: World Scientific. pp. 203–263;
  • Manetti , M. ( 2002 ). Extended deformation functors . Int. Math. Res. Not. 14 : 719 – 756 .
  • Navarro Aznar , V. ( 1987 ). Sur la théorie de Hodge-Deligne . Invent. Math. 90 : 11 – 76 .
  • Pridham , J. P. ( 2010 ). Unifying derived deformation theories . Adv. Math. 224 ( 3 ): 772 – 826 .
  • Sernesi , E. ( 2006 ). Deformations of Algebraic Schemes . Grundlehren der mathematischen Wissenschaften , 334. New York–Berlin : Springer-Verlag .
  • Sullivan , D. ( 1977 ). Infinitesimal computations in topology . Inst. Hautes Études Sci. Publ. Math. 47 : 269 – 331 .
  • Whitney , H. ( 1957 ). Geometric Integration Theory . Princeton , NJ : Princeton University Press .
  • Communicated by C. Cibils.

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