Kuranishi homology and Kuranishi cohomology

Preprint English OPEN
Joyce, Dominic;
  • Subject: Mathematics - Symplectic Geometry
    arxiv: Mathematics::Algebraic Geometry | Mathematics::Complex Variables | Mathematics::Symplectic Geometry

A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. Let Y be an orbifold and R a commutative ring or Q-algebra. We define tw... View more
  • References (24)
    24 references, page 1 of 3

    (b) Let (U, Γ, φ), (V, Δ, ψ), p ∈ φ(U/Γ) ∩ ψ(V /Δ), (Up, Γp, φp), (Vp, Δp, ψp), ρp : Γp → Δp and σp : Up → Vp be as in Definition 2.9, and (U, Γ, φ), (V, Δ, ψ) lift to (EU , Γ, φˆ), (EV , Δ, ψˆ) on E with projections πU : EU → U , πV : EV → V as in (a). Set EUp = πU−1(Up), EVp = πV−1(Vp), so that EUp , EVp are vector bundles over Up, Vp with projections πU : EUp → Up,

    [5] M.F. Atiyah, Bordism and cobordism, Proc. Camb. Phil. Soc. 57 (1961), 200-208.

    [6] K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), 601-617. alg-geom/9601011.

    [7] K. Behrend, Cohomology of stacks, pages 249-294 in E. Arbarello, G. Ellingsrud and L. Goettsche, editors, Intersection theory and moduli, ICTP Lect. Notes volume XIX, Trieste, 2004. Available online at http://publications.ictp.it/.

    [8] K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), 45-88. alg-geom/9601010.

    [9] J. Bryan and R. Pandharipande, BPS states of curves in Calabi-Yau 3- folds, Geometry & Topology 5 (2001) 287-318. math.AG/0009025.

    [10] G.E. Bredon, Topology and Geometry, Graduate Texts in Math. 139, Springer-Verlag, New York, 1993.

    [11] M. Chas and D. Sullivan, String Topology, math.DG/9911159, 1999. To appear in Annals of Mathematics.

    [12] W. Chen and Y. Ruan, Orbifold Gromov-Witten theory, pages 25-86 in A. Adem, J. Morava and Y. Ruan, editors, Orbifolds in mathematics and physics, Cont. Math. 310, A.M.S., Providence, RI, 2002. math.AG/0103156.

    [13] W. Chen and Y. Ruan, A new cohomology theory for orbifold, Comm. Math. Phys. 248 (2004), 1-31. math.AG/0004129.

  • Similar Research Results (1)
  • Metrics
Share - Bookmark