Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces

Abstract

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.

arXiv commentv2: 59 pages, exposition improved

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Cited by in corpus (6)

• Twisted Spin cobordism and positive scalar curvature
• Homotopical and operator algebraic twisted K-theory
• Combinatorial parametrised spectra
• A strictly commutative model for the cochain algebra of a space
• Strict algebraic models for rational parametrised spectra I
• Parametrized spectra, a low-tech approach