scholarly journals Operads and Γ-homology of commutative rings

2002 ◽  
Vol 132 (2) ◽  
pp. 197-234 ◽  
Author(s):  
ALAN ROBINSON ◽  
SARAH WHITEHOUSE
Keyword(s):  
Homotopy Theory ◽  
Commutative Rings ◽  
Homology Theory ◽  
Base Change ◽  
Stable Homotopy ◽  
Stable Homotopy Theory ◽  
General Properties ◽  
Quillen Homology

We introduce Γ-homology, the natural homology theory for E∞-algebras, and a cyclic version of it. Γ-homology specializes to a new homology theory for discrete commutative rings, very different in general from André–Quillen homology. We prove its general properties, including at base change and transitivity theorems. We give an explicit bicomplex for the Γ-homology of a discrete algebra, and elucidate connections with 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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