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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 7th 2013

added details to Borel regulator, with discussion of Becker-Gottlieb transfer and the refinement to differential algebraic K-theory by the transfer index conjecture.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeNov 7th 2013
• (edited Nov 7th 2013)

There is also a famous Soulé regulator. In 2004 Kontsevich gave a related talk (Soulé was in the audience and impressed) about rationality in some computations he was working on with Herbert Gangl at the time concerning the difficult computations in K-theory of fields; there is double grading there zeros above the diagonal and known things below and difficult diagonal terms. Kontsevich related those to some calculations about the moduli space of flat connections and to the boundary. Some integrals related to Chern-Simons theory played a role; there was also an appearance of an interesting transformations (coming back in 5 steps, like in dilogarithm pentagon relations and corresponding cluster algebra examples) relations involving Azumaya algebras (and presumably related to dilogarithm). This work was probably abandoned later but maybe we hear some reflections in upcoming preprint of Kontsevich and Goncharov.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 7th 2013

I guess that refers to Soulé’s “On higher p-adic regulators”?

Maybe you have the time to add soemthing on this to the entry?

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeNov 8th 2013
• (edited Nov 8th 2013)

I do not know which is his original paper, I know of second hand sources only, probably not in one on the $p$-adic case. Maybe there is a hint in his

• C. Soulé, Régulateurs, Seminar Bourbaki, Vol. 1984/85. Asterisque No. 133-134 (1986), 237–253.
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 20th 2014

just for completeness I have added the general definition of regulators for generalized algebraic K-theories here

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 17th 2015

started a new subsection Relation to complex volumes and Bloch group, but not sure yet if I understand the connection. Have marked this as “under construction” for the time being.

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