Topology Advanced Classes
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Mon, 23/02/2009 11:00 |
Neil Strickland (Sheffield) |
Topology Advanced Classes  |
L3 |
| I'll discuss my ongoing attempt to modernise the theory of the image of J. Some features that I would like to have are as follows: 1) Most of the spectra involved in the story should be E_\infty (or strictly commutative) ring spectra, and most of the maps involved should respect this structure. New machinery for dealing with E_\infty rings should be used systematically. 2) As far as possible the constructions used should not depend on arbitrary choices or on gratuitous localisation. 3) The Bernoulli numbers should enter via their primary definition as coefficients of a certain power series. 4) The image of J spectrum should be defined as the Bousfield localisation of S^0 with respect to KO, and other properties or descriptions should be deduced from this one. 5) There should be a clear conceptual explanation for the parallel appearance of Bernoulli numbers in the homotopy groups of J, K(Z) and in spectra related to surgery theory. | |||
