scholarly journals Relative phantom maps and rational homotopy

2020 ◽  
pp. 1
Author(s):  
Daisuke Kishimoto ◽  
Takahiro Matsushita
Keyword(s):  
Rational Homotopy ◽  
Phantom Maps

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 motivic version of the theorem of Fontaine and Wintenberger

2018 ◽  
Vol 155 (1) ◽  
pp. 38-88 ◽  
Author(s):  
Alberto Vezzani
Keyword(s):  
Galois Groups ◽  
Rational Homotopy ◽  
Mixed Characteristic ◽  
Homotopy Invariant ◽  
Analytic Varieties

We establish a tilting equivalence for rational, homotopy-invariant cohomology theories defined over non-archimedean analytic varieties. More precisely, we prove an equivalence between the categories of motives of rigid analytic varieties over a perfectoid field $K$ of mixed characteristic and over the associated (tilted) perfectoid field $K^{\flat }$ of equal characteristic. This can be considered as a motivic generalization of a theorem of Fontaine and Wintenberger, claiming that the Galois groups of $K$ and $K^{\flat }$ are isomorphic.

scholarly journals Two-loop part of the rational homotopy of spaces of long embeddings

2014 ◽  
Vol 23 (04) ◽  
pp. 1450018 ◽  
Author(s):  
Jim Conant ◽  
Jean Costello ◽  
Victor Turchin ◽  
Patrick Weed
Keyword(s):  
Rational Homotopy ◽  
Graph Complexes ◽  
Direct Sum

Arone and Turchin defined graph-complexes computing the rational homotopy of the spaces of long embeddings. The graph-complexes split into a direct sum by the number of loops in graphs. In this paper, we compute the homology of its two-loop part.

An arithmetic characterization of the rational homotopy groups of certain spaces

1979 ◽  
Vol 53 (2) ◽  
pp. 117-133 ◽  
Author(s):  
John B. Friedlander ◽  
Stephen Halperin
Keyword(s):  
Homotopy Groups ◽  
Rational Homotopy

scholarly journals Coformality and rational homotopy groups of spaces of long knots

2008 ◽  
Vol 15 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Greg Arone ◽  
Pascal Lambrechts ◽  
Victor Turchin ◽  
Ismar Volić
Keyword(s):  
Homotopy Groups ◽  
Rational Homotopy
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