Algebraic & Geometric Topology

Relative Thom spectra via operadic Kan extensions

Jonathan Beardsley

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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

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

Keywords
Thom spectra infinity category cobordism cobordism spectra

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.