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 definitions 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 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 object 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
   • CommentTimeJun 9th 2022
   • (edited Jun 9th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexGiven the recent edits, allow me to ask: * Has anyone looked into formalizing [[topological K-theory]] in homotopy type theory? We are specifically after [[twisted equivariant K-theory]], for which it would be important to have not any construction of [[KU]], but to have specifically the space of *[[Fredholm operators]]* axiomatized as a topological (real-cohesive) 0-type, whose [[shape modality|shape]] would give $KU$. Does this seem feasible, to formalized spaces of [[Fredholm operators]] in (real-)cohesive homotopy type theory, and proceed from there to a discussion of topological K-theory? Has anything in the direction been looked at before (separable Hilbert spaces, bounded linear operators, ... in HoTT)?

   Given the recent edits, allow me to ask:

   • Has anyone looked into formalizing topological K-theory in homotopy type theory?

   We are specifically after twisted equivariant K-theory, for which it would be important to have not any construction of KU, but to have specifically the space of Fredholm operators axiomatized as a topological (real-cohesive) 0-type, whose shape would give $KU$.

   Does this seem feasible, to formalized spaces of Fredholm operators in (real-)cohesive homotopy type theory, and proceed from there to a discussion of topological K-theory? Has anything in the direction been looked at before (separable Hilbert spaces, bounded linear operators, … in HoTT)?