#### 301 Citations

On extensions of a symplectic class

- Mathematics
- 2011

Let F be a fibration on a simply-connected base with symplectic fibre (M, \omega). Assume that the fibre is nilpotent and T^{2k}-separable for some integer k or a nilmanifold. Then our main theorem,… Expand

Cosimplicial versus DG-rings: a version of the Dold–Kan correspondence

- Mathematics
- 2003

Abstract The (dual) Dold–Kan correspondence says that there is an equivalence of categories K : Ch ⩾0 → Ab Δ between nonnegatively graded cochain complexes and cosimplicial abelian groups, which is… Expand

Homological algebra of homotopy algebras

- Mathematics
- 1997

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads,… Expand

Enriched Lie algebras in topology, I

- Mathematics
- 2021

To each path connected space X the Sullivan theory of minimal models associates a commutative differential graded algebra, its minimal model (∧V, d), and with it a graded Lie algebra LX that is the… Expand

A commutative model for PL compactly supported cohomology in characteristic zero

- Mathematics
- 2019

We show that that classical rational homotopy theory in the sense of Sullivan [6] can be extended compactly supported setting. This presents a simplicial version of the compactly supported de Rham… Expand

Operads and Operadic Algebras in Homotopy Theory

- Mathematics
- 2019

This is an expository article about operads in homotopy theory written as a chapter for an upcoming book. It concentrates on what the author views as the basic topics in the homotopy theory of… Expand

The Homotopy Theory of Commutative dg Algebras and Representability Theorems for Lie Algebra Cohomology

- Mathematics
- 2019

Building on the seminal works of Quillen [12] and Sullivan [16], Bousfield and Guggenheim [3] developed a "homotopy theory" for commutative differential graded algebras (cdgas) in order to study the… Expand

Unbased rational homotopy theory:a Lie algebra approach

- Mathematics
- 2015

In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of… Expand

Disconnected rational homotopy theory

- Mathematics
- 2013

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… Expand

Rational homotopy theory

- Mathematics
- 2012

These are lecture notes for a course on rational homotopy theory given at the University of Copenhagen in the fall of 2012.