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29
votes
3answers
2k views

Algebras over the little disks operad

Hello, The so-called "recognition principle" of Boardman-Vogt and May leaves me unsatisfied. My problem is the following: The "recognition principle" says that every "group-like" algebra over the ...
3
votes
2answers
746 views

How to define the equivalence of Maurer-Cartan elements in an $L_{\infty}$-algebra?

First let $L^{\bullet}$ be a pro-nilpotent differential graded Lie algebra (dgla). We have the set of Maurer-Cartan elements in $L^{\bullet}$ ($MC(L^{\bullet})$) which are $\alpha \in L^1$ such that ...
22
votes
2answers
2k views

Why should have Peter May worked with CGWH instead of CGH in “The Geometry of Iterated Loop Space”?

This is a follow-up to Dan Ramras' answer of this question. The following correction can be found in the errata to The Geometry of Iterated Loop space (Page 484 here). The weak Hausdorff rather ...
16
votes
1answer
1k views

Little disks operad and $Gal (\bar {Q}/Q)$

My question is simple: How do the little disks operad and $Gal (\bar {Q}/Q)$ relate? I realize that a huge amount of heavy-machinery can be brought into an answer to this, but I'm struggling ...
2
votes
1answer
210 views

Maps between operads of different arities

Is there a category of operads which allows morphisms which take operations to operations with more or fewer arguments? One example should be when you fix arguments to obtain maps with fewer inputs. ...
9
votes
1answer
233 views

Are $E_n$-operads not formal in characteristic not equal to zero?

This is a short question: Is it just unproven folklore (yet), or is it definitively known that $E_n$-operads are not formal, if the characteristic of the underlying field is not equal to zero?
5
votes
1answer
493 views

Boardman-Vogt tensor product

Let $\mathbf{sSet}$ be the model category of simplicial sets and $\mathbf{Op}$ the model category of symmetric operads. Equipped with Boardman-Vogt tensor product $ \otimes_{BV}$, the category ...
1
vote
0answers
530 views

Recognition principle

Hello, The classical statement of the recognition principle (after Boardman, Vogt, Milgram and May) that I know is: Let $X$ be a (group-like) topological space acted on by the little $n$-discs ...