Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 12th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexthe definition, and highlighting that this coincides with Chen-Ruan cohomology of the global quotient orbifold, and with Bredon cohomology with coefficients in the representation ring functor <a href="https://ncatlab.org/nlab/revision/delocalized+equivariant+cohomology/1">v1</a>, <a href="https://ncatlab.org/nlab/show/delocalized+equivariant+cohomology">current</a>

   the definition, and highlighting that this coincides with Chen-Ruan cohomology of the global quotient orbifold, and with Bredon cohomology with coefficients in the representation ring functor

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 12th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexWhy did they call it 'delocalized'?

   Why did they call it ’delocalized’?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 12th 2020
   • (edited Oct 12th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI haven't seen them admit this, but I suppose it must be meant in contrast to the de Rham cohomology of just the direct sum of the fixed loci (which would be localized to the fixed points), i.e. without taking the quotient by the residual $G$-action (which mixes these loci and hence "de-localizes" them). In any case, this choice of terminology probably contributed to keeping the [[incarnations of rational equivariant topological K-theory -- table|true nature]] of the theory a public mystery.

   I haven’t seen them admit this, but I suppose it must be meant in contrast to the de Rham cohomology of just the direct sum of the fixed loci (which would be localized to the fixed points), i.e. without taking the quotient by the residual $G$-action (which mixes these loci and hence “de-localizes” them).

   In any case, this choice of terminology probably contributed to keeping the true nature of the theory a public mystery.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 12th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThanks!

   Thanks!

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 14th 2021
   • (edited Mar 14th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Richard Szabo]], [[Alessandro Valentino]], Section 4.3 of: _Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory_, Commun. Math. Phys. 294:647-702, 2010 ([arXiv:0710.2773](https://arxiv.org/abs/0710.2773)) <a href="https://ncatlab.org/nlab/revision/diff/delocalized+equivariant+cohomology/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/delocalized+equivariant+cohomology/3">v3</a>, <a href="https://ncatlab.org/nlab/show/delocalized+equivariant+cohomology">current</a>

   added pointer to:

   • Richard Szabo, Alessandro Valentino, Section 4.3 of: Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory, Commun. Math. Phys. 294:647-702, 2010 (arXiv:0710.2773)

   diff, v3, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMar 14th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * {#MislinValette03} [[Guido Mislin]], [[Alain Valette]], _Proper Group Actions and the Baum-Connes Conjecture_, Advanced Courses in Mathematics CRM Barcelona, Springer 2003 ([doi:10.1007/978-3-0348-8089-3](https://link.springer.com/book/10.1007/978-3-0348-8089-3)) <a href="https://ncatlab.org/nlab/revision/diff/delocalized+equivariant+cohomology/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/delocalized+equivariant+cohomology/4">v4</a>, <a href="https://ncatlab.org/nlab/show/delocalized+equivariant+cohomology">current</a>

   added pointer to:

   • {#MislinValette03} Guido Mislin, Alain Valette, Proper Group Actions and the Baum-Connes Conjecture, Advanced Courses in Mathematics CRM Barcelona, Springer 2003 (doi:10.1007/978-3-0348-8089-3)

   diff, v4, current