Dendroidal Segal spaces and ∞-operads

Two Models for the Homotopy Theory of ∞-operads

We compare two models for ∞-operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison results already in the literature, this implies that all known models for ∞-operads are equivalent — for instance, it follows that the homotopy theory of Lurie’s ∞-operads is equivalent to that of dendroidal sets and that of...

1.2 Segal Spaces and Complete Segal Spaces.............................. 11

1.2 Segal Spaces and Complete Segal Spaces.............................. 11

Operads and Knot Spaces

Let Em denote the space of embeddings of the interval I = [−1, 1] in the cube I with endpoints and tangent vectors at those endpoints fixed on opposite faces of the cube, equipped with an isotopy through immersions to the unknot – see Definition 5.1. By Proposition 5.17, Em is homotopy equivalent to Emb(I, I) × Imm(I, I). In [26], McClure and Smith define a cosimplicial object O• associated to ...

Moduli Spaces and Formal Operads

Let M g,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations which relate the different moduli spaces identifying marked points, the family (M g,l) g,l is a modular operad of projective smooth Deligne-Mumford stacks, M. In this paper we prove that the modular operad of singular chains C * (M; Q) is formal; so it is weakly equivalent to the modula...