International Mathematics Research Notices

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn041, 35 pages, doi:10.1093/imrn/rnn041 published on April 25, 2008

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Strong homotopy inner product of an A-algebra

Cheol-Hyun Cho

Department of Mathematical Sciences, Seoul National University, San 56-1, Shinrimdong, Gwanak-gu, Seoul, South Korea

Correspondence: Correspondence to be sent to: chocheol{at}snu.ac.kr

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A-algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the notion of a nonconstant symplectic structure on the corresponding formal noncommutative supermanifold. We show that (open Gromov–Witten type) potential for a cyclic filtered A-algebra is invariant under the cyclic filtered A-homomorphism up to reparameterization, cyclization, and a constant addition, generalizing the work of Kajiura.

References

1. Cho C.-H. "Counting real J-holomorphic discs and spheres in dimension four and six." Journal of Korean Math. Soc. (2006) preprint arXiv:math/0604502.
2. Costello K. "Topological conformal field theories and Calabi-Yau categories". Advances in Mathematics (2007) 210(1):165–214.[CrossRef][ISI]
3. Fukaya K., Oh Y.-G., Ohta H., Ono K. "Lagrangian intersection Floer theory-anomaly and obstruction". (2000) Kyoto University preprint.
4. Ginzburg V. "Lectures on non-commutative geometry". (2005) preprint arXiv:math/0506603.
5. Getzler E., Jones J. "A-algebras and the cyclic bar complex". Illinois Journal of Mathematics (1990) 34(2):256–83.[ISI]
6. Kontsevich M. "Formal (non)Commutative Symplectic Geometry." (1993) The Gelfand Mathematical Seminars 1990–1992. Boston, MA: Birkhauser. 173–87.
7. Kontsevich M., Soibelman Y. "Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I." (2006) preprint arXiv:math/0606241.
8. Kajiura H. "Noncommutative homotopy algebras associated with open strings". Reviews in Mathematical Physics (2007) 1:1–99.
9. Tradler T. "Infinity inner products". (2001) preprint arXiv:math/0108027.Tradler T., Zeinalian M. "Infinity structure of Poincare duality spaces". Algebraic & Geometric Topology (2007) 7:233–60.[CrossRef]
11. Solomon J. "Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions". (2006) preprint arXiv:math/0606429.
12. Welschinger J.-Y. "Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants". Duke Mathematical Journal (2005) 127(1):89–121.[CrossRef][ISI]

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions How to cite this article Google Scholar Articles by Cho, C.-H. Social Bookmarking          What's this?