FQFT and cohomology
For a useful exposition of this see (Tolland).
here are some seminar notes:
An exposition of GW theory as a TCFT is at
Discussion in the context of geometric quantization is in
See also the references at A-model.
A discussion by quantization of quadratic Hamiltonians is in
M. Kontsevich, Yu. Manin, Gromov-Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994), no. 3, 525–562 (euclid).
Yuri Manin, Frobenius manifolds, quantum cohomology and moduli spaces, Amer. Math. Soc., Providence, RI, 1999,
W. Fulton, R. Pandharipande, Notes on stable maps and quantum cohomology, in: Algebraic Geometry- Santa uz 1995 ed. Kollar, Lazersfeld, Morrison. Proc. Symp. Pure Math. 62, 45–96 (1997)
J Robbin, D A Salamon, A construction of the Deligne-Mumford orbifold, J. Eur. Math. Soc. (JEMS) 8 (2006), no. 4, 611–699 (arxiv; pdf at JEMS); corrigendum J. Eur. Math. Soc. (JEMS) 9 (2007), no. 4, 901–905 (pdf at JEMS).
J Robbin, Y Ruan, D A Salamon, The moduli space of regular stable maps, Math. Z. 259 (2008), no. 3, 525–574 (doi).
Martin A. Guest, From quantum cohomology to integrable systems, Oxford Graduate Texts in Mathematics, 15. Oxford University Press, Oxford, 2008. xxx+305 pp.
Joachim Kock, Israel Vainsencher, An invitation to quantum cohomology. Kontsevich’s formula for rational plane curves, Progress in Mathematics, 249. Birkhäuser Boston, Inc., Boston, MA, 2007. xiv+159 pp.
Dusa McDuff, Dietmar Salamon, Introduction to symplectic topology, 2 ed. Oxford Mathematical Monographs 1998. x+486 pp.
Sheldon Katz, Enumerative geometry and string theory, Student Math. Library 32. IAS/Park City AMS & IAS 2006. xiv+206 pp.
Eleny-Nicoleta Ionel, Thomas H. Parker, Relative Gromov-Witten invariants, Ann. of Math. (2) 157 (2003), no. 1, 45–96 (doi).
Oliver Fabert, Floer theory, Frobenius manifolds and integrable systems, (arxiv/1206.1564)
A generalization is discussed in
Expositions and summaries of this are in
A review with further pointers is in
Further investigation of these stacky Chow motives then appears in