Batalin-Vilkovisky Algebras and Two-Dimensional Topological Field Theories

  title={Batalin-Vilkovisky Algebras and Two-Dimensional Topological Field Theories},
  author={E. Getzler},
  • E. Getzler
  • Published 1994
By a Batalin-Vilkovisky algebra, we mean a graded commutative algebra A, together with an operator A: A. -+ A. +1 such that A 2 = 0, and \_A,d\ — Aa is a graded derivation of A for all a e A. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads. Batalin-Vilkovisky algebras are a new type of algebraic… CONTINUE READING
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Showing 1-10 of 23 references

The geometry of iterated loop spaces

  • J. P. May
  • Lecture Notes in Mathematics,
  • 1972
Highly Influential
8 Excerpts

The cohomology ring of the colored braid group

  • V. I. Arnold
  • Mat. Zametki 5, 227-231
  • 1969
Highly Influential
6 Excerpts

Geometry of Batalin-Vilkovisky quantization

  • A. Schwarz
  • Preprint hep-th/9205088, University of California…
  • 1992
Highly Influential
5 Excerpts

Infinitesimal structures of moduli space of G-bundles

  • A. Beilinson, V. Ginzburg
  • Duke Math. J. 66, 63-74
  • 1992
Highly Influential
3 Excerpts

On the structure of the topological phase of two-dimensional gravity

  • E. Witten
  • Nucl. Phys. B340, 281-332
  • 1990
Highly Influential
9 Excerpts

The anti-bracket formalism

  • E. Witten
  • Mod. Phys. Lett. A5, 487-494
  • 1990
Highly Influential
8 Excerpts

Braids, links and mapping class groups

  • J. S. Birman
  • Ann. Math. Studies,
  • 1974
Highly Influential
3 Excerpts

Homotopy invariant algebraic structures on topological spaces

  • J. M. Boardman, R. M. Vogt
  • Lecture Notes in Mathematics,
  • 1973
Highly Influential
4 Excerpts

Koszul resolutions

  • S. B. Priddy
  • Trans. Am. Math. Soc. 152, 39-60
  • 1970
Highly Influential
3 Excerpts

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