Abstract
Some time ago B. Feigin, V. Retakh and I had tried to understand a remark of J. Stasheff [S1] on open string theory and higher associative algebras [S2]. Then I found a strange construction of cohomology classes of mapping class groups using as initial data any differential graded algebra with finite-dimensional cohomology and a kind of Poincaré duality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Axelrod and I. M. Singer, Chern-Simons Perturbation Theory, M. I. T. preprint (October 1991).
D. Bar-Natan, On the Vassiliev Knot Invariants, Harvard preprint (August 1992).
K. S. Brown, Cohomology of Group, Graduate Texts in Mathematics; 87, Springer, Berlin, Heidelberg, New York, 1982.
M. Culler and K. Vogtmann, Moduli of Graphs and Automorphisms of Free Groups, Invent. Math. 84 (1986), 91–119.
J. Cuntz, D. Quillen, Algebra extensions and nonsingularity (to appear).
V. G. Drinfel’d, On quasitriangular Quasi-Hopf algebras and a group closely connected with Gal(¯Q/Q), Leningrad Math. J. 2 (1991), 829–860.
D. B. Fuks, Cohomology of Infinite-Dimensional Lie Algebras, Consultants Bureau, New York and London, 1986.
I. M. Gelfand and D. B. Fuks, Cohomology of Lie algebras of formal vector fields, Izv. Akad. Nauk SSSR, Ser. Mat. 34 (1970), no. 2, 322–337.
I. M. Gelfand and O. Mathieu, On the Cohomology of the Lie Algebra of Hamiltonian Vector Fields, preprint RIMS-781 (1991).
V. Ginzburg and M. Kapranov, Koszul duality for quadratic operads, to appear.
V. W. Guillemin and S. D. Shnider, Some stable results on the cohomology of classical infinite-dimensional Lie algebras, Trans. Am. Math. Soc. 179 (1973), 275–280.
J. Harer, The cohomology of the moduli space of curves, LNM 1337, Springer, 138–221.
R. C. Penner, The decorated Teichmü ller space of punctured surfaces, Commun. Math. Phys. 113 (1987), 299–339.
D. Quillen, Rational Homotopy Theory, Ann. Math. 90 (1969), 205–295.
J. Stasheff, An almost groupoid structure for the space of (open) strings and implications for string field theory, “Advances in Homotopy Theory” (Cortona, June 1988), LMS Lecture Notes Serties, vol. 139, 1989, pp. 165–172.
J. Stasheff, On the homotopy associativity of H-Spaces I, II, Trans. AMS 108 (1963), 275–312.
K. Strebel, Quadratic differentials, Springer, Berlin, Heidelberg, New York, 1984.
D. Sullivan, Infinitesimal computations in topology, Publ. I. H. E. S. 47 (1978), 269–331.
V. Vassiliev, Complements to Discriminants of Smooth Maps: Topology and Applications, Amer. Math. Soc. Press, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kontsevich, M. (1993). Formal (Non)-Commutative Symplectic Geometry. In: Gelfand, I.M., Corwin, L., Lepowsky, J. (eds) The Gelfand Mathematical Seminars, 1990–1992. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0345-2_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0345-2_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6717-1
Online ISBN: 978-1-4612-0345-2
eBook Packages: Springer Book Archive