Disconnected Rational Homotopy Theory
نویسندگان
چکیده
We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other one on complete differential graded Lie algebras. As an application of the developed technology we obtain results on the structure of Maurer-Cartan spaces of complete differential graded Lie algebras.
منابع مشابه
Derived Algebraic Geometry XIII: Rational and p-adic Homotopy Theory
1 Rational Homotopy Theory 4 1.1 Cohomological Eilenberg-Moore Spectral Sequences . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 k-Rational Homotopy Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Rational Homotopy Theory and E∞-Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Differential Graded Lie Algebras . . . . . . . . . . ...
متن کاملar X iv : m at h / 00 10 12 6 v 1 [ m at h . A T ] 1 2 O ct 2 00 0 RATIONAL OBSTRUCTION THEORY AND RATIONAL HOMOTOPY SETS
We develop an obstruction theory for homotopy of homomorphisms f, g : M → N between minimal differential graded algebras. We assume that M = ΛV has an obstruction decomposition given by V = V0⊕V1 and that f and g are homotopic on ΛV0. An obstruction is then obtained as a vector space homomorphism V1 → H(N ). We investigate the relationship between the condition that f and g are homotopic and th...
متن کاملAn Algebraic Model for Rational S-equivariant Stable Homotopy Theory
Greenlees defined an abelian category A whose derived category is equivalent to the rational S1-equivariant stable homotopy category whose objects represent rational S1equivariant cohomology theories. We show that in fact the model category of differential graded objects in A models the whole rational S1-equivariant stable homotopy theory. That is, we show that there is a Quillen equivalence be...
متن کاملRationalized Evaluation Subgroups of a Map Ii: Quillen Models and Adjoint Maps
Let ω : map(X, Y ; f) → Y denote a general evaluation fibration. Working in the setting of rational homotopy theory via differential graded Lie algebras, we identify the long exact sequence induced on rational homotopy groups by ω in terms of (generalized) derivation spaces and adjoint maps. As a consequence, we obtain a unified description of the rational homotopy theory of function spaces, at...
متن کاملQuillen Spectral Sequences in Homology and Rational Homotopy of Cofibrations
We construct Quillen type spectral sequences in homology and rational homotopy for coobration sequences which are Eckmann-Hilton dual to analogous ones for bration sequences. These spectral sequences are constructed by direct ltrations of the Adams cobar construction. We also prove various collapsing theorems generalizing results of Clark and Smith in the case of a wedge of 1-connected nicely p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015