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1. • CommentRowNumber1.
   • CommentAuthoradeelkh
   • CommentTimeJan 5th 2015
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexCreated the page [[semi-topological K-theory]].

   Created the page semi-topological K-theory.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 5th 2015
   • (edited Jan 6th 2015)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for this! Semitopological K-theory smells like it must be related to the discussion of K-theory in the differential cohomology hexagon [here](http://ncatlab.org/nlab/show/differential+cohomology+diagram#DifferentialKTheory), following Bunke-Nikolaus-Völkl. There one also considers K-theory sheaves, then forms their $\mathbb{R}^1$-localization (shape modality $\Pi$!) and finds topological K-theory. In fact what is discussed there very much smells like it wants to be a sheaf over a product of geometries modeled on $\mathbb{R}^1$ and on $\mathbb{A}^1$ as in [[differential algebraic K-theory]], which makes the conceptual similarity to semitopoligical K-theory even stronger.

   Thanks for this!

   Semitopological K-theory smells like it must be related to the discussion of K-theory in the differential cohomology hexagon here, following Bunke-Nikolaus-Völkl. There one also considers K-theory sheaves, then forms their $\mathbb{R}^1$-localization (shape modality $\Pi$!) and finds topological K-theory.

   In fact what is discussed there very much smells like it wants to be a sheaf over a product of geometries modeled on $\mathbb{R}^1$ and on $\mathbb{A}^1$ as in differential algebraic K-theory, which makes the conceptual similarity to semitopoligical K-theory even stronger.

3. • CommentRowNumber3.
   • CommentAuthoradeelkh
   • CommentTimeJan 6th 2015
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   Author: adeelkh
   Format: MarkdownItexInteresting, thanks for the pointer! I will have to take a look at BNV.

   Interesting, thanks for the pointer! I will have to take a look at BNV.