Relative Thom spectra via operadic Kan extensions

Beardsley, Jonathan

doi:10.2140/agt.2017.17.1151

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Relative Thom spectra via operadic Kan extensions

Jonathan Beardsley

Algebraic & Geometric Topology 17 (2017) 1151–1162

DOI: 10.2140/agt.2017.17.1151

Abstract

We show that a large number of Thom spectra, that is, colimits of morphisms $B G \to B {GL}_{1} (S)$ , can be obtained as iterated Thom spectra, that is, colimits of morphisms $B G \to B {GL}_{1} (M f)$ for some Thom spectrum $M f$ . This leads to a number of new relative Thom isomorphisms, for example $M U [6, \infty) \land_{M String} M U [6, \infty) ≃ M U [6, \infty) \land S [B^{3} Spin]$ . As an example of interest to chromatic homotopy theorists, we also show that Ravenel’s $X (n)$ filtration of $M U$ is a tower of intermediate Thom spectra determined by a natural filtration of $B U$ by subbialagebras.

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

Keywords

Thom spectra, infinity category, cobordism, cobordism spectra

Mathematical Subject Classification 2010

Primary: 55N22, 55P42

Supplementary material

Errata posted on 26 May 2017

References

Publication

Received: 31 March 2016

Revised: 21 August 2016

Accepted: 24 September 2016

Published: 14 March 2017

Authors

Jonathan Beardsley
Department of Mathematics University of Washington C-138 Padelford Seattle, WA 98195 United States
http://www.math.washington.edu/~jbeards1

Volume 17, issue 2 (2017)