MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES

Autor: FABIAN HEBESTREIT, STEFFEN SAGAVE, CHRISTIAN SCHLICHTKRULL
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Forum of Mathematics, Sigma, Vol 8 (2020)
Druh dokumentu: article
ISSN: 2050-5094
DOI: 10.1017/fms.2020.11
Popis: 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 $\infty$-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.
Databáze: Directory of Open Access Journals