English

Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces

Algebraic Topology 2020-03-20 v2 K-Theory and Homology

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.

Keywords

Cite

@article{arxiv.1904.01824,
  title  = {Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces},
  author = {Fabian Hebestreit and Steffen Sagave and Christian Schlichtkrull},
  journal= {arXiv preprint arXiv:1904.01824},
  year   = {2020}
}

Comments

v2: 59 pages, exposition improved