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Relative Thom spectra via operadic Kan extensions

Jonathan Beardsley

Algebraic & Geometric Topology 17 (2017) 1151–1162

We show that a large number of Thom spectra, that is, colimits of morphisms BG BGL1(S), can be obtained as iterated Thom spectra, that is, colimits of morphisms BG BGL1(Mf) for some Thom spectrum Mf. This leads to a number of new relative Thom isomorphisms, for example MU[6,) M StringMU[6,) MU[6,) S[B3 Spin]. 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 subbialagebras.

An errata was posted on 26 May 2017 in an online supplement.

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Thom spectra, infinity category, cobordism, cobordism spectra
Mathematical Subject Classification 2010
Primary: 55N22, 55P42
Supplementary material

Errata posted on 26 May 2017

Received: 31 March 2016
Revised: 21 August 2016
Accepted: 24 September 2016
Published: 14 March 2017
Jonathan Beardsley
Department of Mathematics
University of Washington
C-138 Padelford
Seattle, WA 98195
United States