Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorPatrick
    • CommentTimeDec 26th 2015

    I recently found the nLab cohomology entry and was intrigued by the claim that any reasonable kind of cohomology ought to “have a natural interpretation in terms of connected components of hom-spaces in (,1)(\infty,1)-categories.”

    Does quantum cohomology, as developed by Fulton and Pandharipande in their Notes on stable maps and quantum cohomology, fit into this scheme? It is not obvious to me that it does. I checked the entries on quantum sheaf cohomology and Gromov-Witten invariants, but they do not address this question.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 4th 2016

    Not sure if this helps, but just for the record I’ll say that what is called quantum cohomology is a certain graded direct sum of sheaf cohomology groups, and equipped with a certain Frobenius algebra structure. So to some extent this is just plain sheaf cohomology with extra structure. Of course it may still be that this has a nice more abstract description, not sure.