## Algebraic & Geometric Topology

### Relative Thom spectra via operadic Kan extensions

Jonathan Beardsley

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1508431457

Digital Object Identifier
doi:10.2140/agt.2017.17.1151

Mathematical Reviews number (MathSciNet)
MR3623685

Zentralblatt MATH identifier
06698212

#### Citation

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. https://projecteuclid.org/euclid.agt/1508431457

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#### Corrections

• Errata posted on 26 May 2017.