In a comment on Tom Goodwillie's question about relating the Alexander polynomial and the Iwasawa polynomial, Minhyong Kim makes the cryptic but tantalizing statement:

In brief, the current view is that the Iwasawa polynomial=p-adic L-function should be viewed as a path in K-theory space.

As somebody who has been trying, for a long time, to understand the Alexander polynomial, and who believes there is something "more basic" underlying its appearances in mathematics in various guises (my particular interest has to do with why it turns up as the wheels part of the Kontsevich invariant, as per Melvin-Morton-Rozansky), I'd really like to understand this comment.

Question: What is "K-theory space" supposed to be, and why should a path in it be a natural object to be examining? And why should we expect such a thing to give equivalent data to the Iwasawa polynomial/ Alexander polynomial?

In a comment on Tom Goodwillie's question about relating the Alexander polynomial and the Iwasawa polynomial, Minhyong Kim makes the cryptic but tantalizing statement:

In brief, the current view is that the Iwasawa polynomial=p-adic L-function should be viewed as a path in K-theory space.

As somebody who has been trying, for a long time, to understand the Alexander polynomial, and who believes there is something "more basic" underlying its appearances in mathematics in various guises (my particular interest has to do with why it turns up as the wheels part of the Kontsevich invariant, as per Melvin-Morton-Rozansky), I'd really like to understand this comment.

Question: What is "K-theory space" supposed to be, and why should a path in it be a natural object to be examining? And why should we expect such a thing to give equivalent data to the Iwasawa polynomial/ Alexander polynomial?