All Questions
Tagged with rational-homotopy-theory reference-request
8 questions
18
votes
1
answer
991
views
Higher homotopy algebraic structure on the homology of an operad
Given a DGA $A$, then by standard techniques such as homological perturbation theory, the ring structure on the homology $H(A)$ extends to a minimal $A_\infty$-algebra structure such that $H(A)$ is ...
- 6,229
12
votes
2
answers
799
views
Reference for functors in Kadeishvili's C_\infty paper
In his paper Cohomology $C_\infty$-algebra and rational homotopy type, Tornike Kadeishvili describes how the rational cohomology of a simply-connected space carries the structure of a $C_\infty$-...
- 35.9k
11
votes
1
answer
804
views
rational homotopy of a manifold
Given a finite dim rational homotopy type satisfying Poincaré duality,
what is the best reference to when it is the rational homotopy type of a fin dim manifold?
- 3,880
9
votes
1
answer
253
views
Almost free circle actions on spheres
$\DeclareMathOperator{\Fix}{\operatorname{Fix}}$I am looking for any reference regarding the following problem:
Problem: Consider a smooth almost-free action of $S^1$ on a smooth sphere $S^n$. Then ...
- 1,452
8
votes
0
answers
134
views
Rational homotopy type of Hilbert scheme components
What is known about rational homotopy type of irreducible component of $Hilb^n(\mathbb C^k)$ containing configuration space? I've searched arXiv for a while and found nothing but surmise that Betti ...
- 4,600
5
votes
1
answer
634
views
What's a good reference for the following obstruction theory yoga?
Fix a colored operad, which I will leave implicit, and a field $\mathbb K$ of characteristic $0$. By algebra in this post I will mean a dg algebra over $\mathbb K$ for the given colored operad. I ...
- 54.6k
4
votes
0
answers
108
views
Finite spatial realization of relative minimal sullivan models
In their book "Algebraic Models in Geometry" (Felix, Oprea, Tanre) the authors claim that:
"Each finite type relative minimal cdga $(∧V ⊗∧W,D)$ is the relative minimal model of a fibration $p: E → B$ ...
- 404
3
votes
0
answers
145
views
Formality of Sullivan Representatives
Suppose we have a map $f : \mathcal{A} \to \mathcal{B}$ between two formal, simply connected CDGAs, with induced map on cohomology $H(f) : H(\mathcal{A}) \to H(\mathcal{B})$. Further, suppose we have ...
- 285