A functorial model for iterated Snaith splitting with applications to calculus of functors

1998 ◽  
pp. 1-30 ◽  
Author(s):  
Gregory Arone ◽  
Marja Kankaanrinta
Keyword(s):  
Calculus Of Functors

scholarly journals Goodwillie's calculus of functors and higher topos theory

2018 ◽  
Vol 11 (4) ◽  
pp. 1100-1132 ◽  
Author(s):  
M. Anel ◽  
G. Biedermann ◽  
E. Finster ◽  
A. Joyal
Keyword(s):  
Topos Theory ◽  
Calculus Of Functors

scholarly journals Calculus of functors, operad formality, and rational homology of embedding spaces

2007 ◽  
Vol 199 (2) ◽  
pp. 153-198 ◽  
Author(s):  
Gregory Arone ◽  
Pascal Lambrechts ◽  
Ismar Volić
Keyword(s):  
Rational Homology ◽  
Calculus Of Functors ◽  
Embedding Spaces

scholarly journals EQUIVARIANT CALCULUS OF FUNCTORS AND-ANALYTICITY OF REAL ALGEBRAIC -THEORY

2015 ◽  
Vol 15 (4) ◽  
pp. 829-883 ◽  
Author(s):  
Emanuele Dotto
Keyword(s):  
Finite Group ◽  
Classical Result ◽  
Algebraic Theory ◽  
Calculus Of Functors ◽  
Goodwillie Calculus ◽  
A Finite Group ◽  
Zero Extension ◽  
Homotopy Functors

We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial $G$-sets to symmetric $G$-spectra, where $G$ is a finite group. We extend a notion of $G$-linearity suggested by Blumberg to define stably excisive and ${\it\rho}$-analytic homotopy functors, as well as a $G$-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected $G$-maps to $G$-equivalences. It is analogous to the classical result of Goodwillie that ‘functors with zero derivative are locally constant’. As the main example, we show that Hesselholt and Madsen’s Real algebraic $K$-theory of a split square zero extension of Wall antistructures defines an analytic functor in the $\mathbb{Z}/2$-equivariant setting. We further show that the equivariant derivative of this Real $K$-theory functor is $\mathbb{Z}/2$-equivalent to Real MacLane homology.

scholarly journals Calculus of functors and model categories, II

2014 ◽  
Vol 14 (5) ◽  
pp. 2853-2913 ◽  
Author(s):  
Georg Biedermann ◽  
Oliver Röndigs
Keyword(s):  
Model Categories ◽  
Calculus Of Functors

The Goodwillie Calculus of Functors

2004 ◽  
pp. 873-914
Author(s):  
Thomas Goodwillie ◽  
Randy McCarthy
Keyword(s):  
Calculus Of Functors ◽  
Goodwillie Calculus

scholarly journals Calculus of functors and model categories

2007 ◽  
Vol 214 (1) ◽  
pp. 92-115 ◽  
Author(s):  
Georg Biedermann ◽  
Boris Chorny ◽  
Oliver Röndigs
Keyword(s):  
Model Categories ◽  
Calculus Of Functors

scholarly journals UNITARY FUNCTOR CALCULUS WITH REALITY

2021 ◽  
pp. 1-34
Author(s):  
NIALL TAGGART
Keyword(s):  
Homotopy Theory ◽  
Model Structure ◽  
Classifying Space ◽  
The Real ◽  
Calculus Of Functors ◽  
Taylor Tower ◽  
Orthogonal Calculus

Abstract We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study ‘functors with reality’ such as the Real classifying space functor, $\BU_\Bbb{R}(-)$ . The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of $C_2 \ltimes \U(n)$ . We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of $C_2 \ltimes \U(n)$ and a model structure on the category of input functors which captures the homotopy theory of the n-th layer of the Taylor tower.

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