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Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces

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 infinity-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.

preprint2020arXivOpen access
Fabian HebestreitSteffen SagaveChristian Schlichtkrull
math.ATmath.KT
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Fabian HebestreitSteffen SagaveChristian Schlichtkrull

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