9
votes
Accepted
Is there a proof of the formality of configuration spaces of Euclidean spaces that do not involve operads?
When $n$ is even these spaces are complex algebraic varieties, so the cohomology comes with a mixed Hodge structure. Moreover, this mixed Hodge structure is pure: the cohomology ring is generated in ...
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4
votes
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$\mathbb Z$-formality of spheres
Consider the simplicial set $\def\S{{\bf S}} \def\Sing{\mathop{\rm Sing}} \S^n=Δ^n/∂Δ^n$, which has exactly two nondegenerate simplices: a 0-simplex and an $n$-simplex.
Consider the map $\S^n→\Sing S^...
- 37.8k
3
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Alternative to Kontsevich formality
You might want to have a look at §2.2 of An $L_\infty$ algebra structure on polyvector fields by Boris Shoikhet, where Boris constructs an exotic $L_\infty$-structure on poly-vector fields on a (...
- 8,385
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vote
Accepted
Are the two families of Johnson invariants of the Torelli groups related beyond the first one?
Knowing $\text{gr}\ T$ only tells you about cup products and higher Massey products on $H^1(T;\mathbb{Q})$. Beyond that, there is no real relationship between $\text{gr}\ T$ and $H_{\ast}(T)$.
Your ...
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Is there a proof of the formality of configuration spaces of Euclidean spaces that do not involve operads?
I only recently saw this now old post, but in case it's useful to anyone, I believe the proof of the formality of $\mathrm{Conf}_k(\mathbb{R}^n)$ for $n\geq 3$ given in [Lambrechts–Volic] applies at ...
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