I am giving *fiber integration in K-theory* a dedicated entry.

One section *In operator K-theory* used to be a subsection of *fiber integration in generalized cohomology*, and I copied it over.

Another section *In terms of bundles of Fredholm operators* I have now started to write.

I’d be trying to write out a more detailed exposition of how fiber integration in twisted generalized cohomology/twisted Umkehr maps are axiomaized in linear homotopy-type theory.

To start with I produced a dictionary table, for inclusion in relevant entries:

]]>created an entry *twisted Umkehr map*. The material now has some overlap with what I just put into *Pontrjagin-Thom collapse map*. But that doesn’t hurt, I think.

started fiber integration

]]>Can we view an integral somehow as transfinite composition of “small” arrows, in a rigorous (but possibly nonstandard) way?

For example, if we view a real 1-form as a functor with values in $B\mathbb{R}$, is its integration along a curve a transfinite composition of its values at all the tangent vectors of the curve?

I don’t know if the question is clear enough, in case it isn’t, feel free to ask. (It may also be that none of this makes any sense.)

]]>gave *virtual fundamental class* an Idea-section (feel free to improve) and added a bunch of pointers to the literature in the References-section

seeing the announcement of that diffiety summer school made me think that we should have a dedicated entry titled *cohomological integration* which points to the aspects of this discussed already elswhere on the nLab, and which eventually lists dedicated references, if any. So I created a stub.

Does anyone know if there is a published reference to go with the relevant diffiety-school page ?

]]>created stub for *[[Wick's lemma]]*, for the moment just so as to record a pointer to a reference