Enchiridion: Vol. 3 (2017): Jon Beardsley

Jon Beardsley (University of Washington)

User’s Guide
Topic 1: Key insights and organizing principles
Topic 2: Conceptual metaphors and mental imagery
Topic 3: Story of the development
Topic 4: Colloquial summary
(as a single PDF)

Source Paper
Relative Thom spectra via operadic Kan extensions

Source Paper Abstract
We show that a large number of Thom spectra, i.e. colimits of morphisms BG \rightarrow BGL_1(\mathbb{S}), can be obtained as iterated Thom spectra, i.e. colimits of morphisms BG \rightarrow BGL_1(Mf) for some Thom spectrum Mf. This leads to a number of new relative Thom isomorphisms, e.g. MU[6,\infty)\wedge_{MString} MU[6,\infty) \simeq MU[6,\infty) \wedge \mathbb{S}[B^3Spin]. As an example of interest to chromatic homotopy theorists, we also show that Ravenel’s X(n) filtration of MU is a tower of intermediate Thom spectra determined by a natural filtration of BU by sub-bialagebras.

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