Foundations of Stable Homotopy Theory

2020 ◽  
Author(s):  
David Barnes ◽  
Constanze Roitzheim
Keyword(s):  
Homotopy Theory ◽  
Stable Homotopy ◽  
Stable Homotopy Theory

v 1 - and v 2 -Periodicity in Stable Homotopy Theory

1981 ◽  
Vol 103 (4) ◽  
pp. 615 ◽  
Author(s):  
Donald M. Davis ◽  
Mark Mahowald
Keyword(s):  
Homotopy Theory ◽  
Stable Homotopy ◽  
Stable Homotopy Theory

Spectra of derived module homomorphisms

1987 ◽  
Vol 101 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Alan Robinson
Keyword(s):  
Spectral Sequence ◽  
Homotopy Theory ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Stable Homotopy Theory ◽  
Ring Spectrum ◽  
Homotopy Invariant ◽  
New Construction

We introduce a new construction in stable homotopy theory. If F and G are module spectra over a ring spectrum E, there is no well-known spectrum of E-module homomorphisms from F to G. Such a construction would not be homotopy invariant, and therefore would not serve much purpose. We show that, provided the rings and modules have A∞ structures, there is a spectrum RHomE(F, G) of derived module homomorphisms which has very pleasant properties. It is homotopy invariant, exact in each variable, and its homotopy groups form the abutment of a hypercohomology-type spectral sequence.

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