Algebraic & Geometric Topology

Relative Thom spectra via operadic Kan extensions

Jonathan Beardsley

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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.

Article information

Algebr. Geom. Topol., Volume 17, Number 2 (2017), 1151-1162.

Received: 31 March 2016
Revised: 21 August 2016
Accepted: 24 September 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 55P42: Stable homotopy theory, spectra

Thom spectra infinity category cobordism cobordism spectra


Beardsley, Jonathan. Relative Thom spectra via operadic Kan extensions. Algebr. Geom. Topol. 17 (2017), no. 2, 1151--1162. doi:10.2140/agt.2017.17.1151.

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  • Errata posted on 26 May 2017.