H∞ ring spectra via space-level homotopy theory

1986 ◽  
pp. 215-248
Author(s):  
J. E. McClure
Keyword(s):  
Homotopy Theory ◽  
Ring Spectra

scholarly journals MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES

2020 ◽  
Vol 8 ◽  
Author(s):  
FABIAN HEBESTREIT ◽  
STEFFEN SAGAVE ◽  
CHRISTIAN SCHLICHTKRULL
Keyword(s):  
Homotopy Theory ◽  
Companion Paper ◽  
Smash Product ◽  
Algebraic Models ◽  
Thom Spectra ◽  
Ring Spectra ◽  
Symmetric Spectra ◽  
Point Set

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.

On equivariant disconnected rational homotopy theory

2010 ◽  
Vol 17 (2) ◽  
pp. 229-240
Author(s):  
Marek Golasiński
Keyword(s):  
Homotopy Theory ◽  
Weak Equivalence ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Hamiltonian Group ◽  
Simplicial Set ◽  
De Rham

Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

scholarly journals A First Approximation to Homotopy Theory

1953 ◽  
Vol 39 (7) ◽  
pp. 655-660 ◽  
Author(s):  
E. H. Spanier ◽  
J. H. C. Whitehead
Keyword(s):  
Homotopy Theory ◽  
First Approximation
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