15:45
I will describe an extremely easy construction with formal group laws, and a
slightly more subtle argument to show that it can be done in a coordinate-free
way with formal groups. I will then describe connections with a range of other
phenomena in stable homotopy theory, although I still have many more
questions than answers about these. In particular, this should illuminate the
relationship between the Lambda algebra and the Dyer-Lashof algebra at the
prime 2, and possibly suggest better ways to think about related things at
odd primes. The Morava K-theory of symmetric groups is well-understood
if we quotient out by transfers, but somewhat mysterious if we do not pass
to that quotient; there are some suggestions that dilation will again be a key
ingredient in resolving this. The ring $MU_*(\Omega^2S^3)$ is another
object for which we have quite a lot of information but it seems likely that
important ideas are missing; dilation may also be relevant here.