Relative Thom spectra via operadic Kan extensions

Beardsley, Jonathan¹

¹Department of Mathematics, University of Washington, C-138 Padelford, Seattle, WA 98195, United States

Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 1151-1162

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.1151

Classification : 55N22, 55P42
Keywords: Thom spectra, infinity category, cobordism, cobordism spectra

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