Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
Journal article, Peer reviewed
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OriginalversjonForum of Mathematics, Sigma. 2020, 8, e16. 10.1017/fms.2020.11
In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set-level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding ∞-categorical product and allows for convenient constructions of commutative parametrized ring spectra. As an immediate application, we compare various models for generalized Thom spectra. In a companion paper, this approach is used to compare homotopical and operator algebraic models for twisted K-theory.