46 citations · 164 across the 22 of their papers we have counts for
24 papers
Galois actions on surfaces and a higher genus Grothendieck-Teichmüller group
Luciana Basualdo Bonatto, Marcy Robertson
We construct a modular operad of mapping class groupoids modelling the higher-genus Teichmüller tower, with compositions and contractions encoding surface gluing. We p…
Grothendieck-Teichmüller Symmetries of Cyclic Operads and Tangles
Marcy Robertson, Chandan Singh
We identify the profinite Grothendieck-Teichmüller group with the group of homotopy automorphisms of the profinite completion of the cyclic operad of parent…
Genus Zero Kashiwara-Vergne Solutions from Braids
Zsuzsanna Dancso, Iva Halacheva, Guillaume Laplante-Anfossi +2
Using the language of moperads -- monoids in the category of right modules over an operad -- we reinterpret the Alekseev--Enriquez--Torossian construction of Kashiwara--Vergne (KV)…
A knot-theoretic approach to comparing the Grothendieck-Teichmüller and Kashiwara-Vergne groups
Zsuzsanna Dancso, Tamara Hogan, Marcy Robertson
Homomorphic expansions are combinatorial invariants of knotted objects, which are universal in the sense that all finite-type (Vassiliev) invariants factor through them. Homomorphi…
Lecture Notes on Modular Infinity Operads and Grothendieck-Teichmueller Theory
Olivia Borghi, Marcy Robertson
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus…
A topological characterisation of the Kashiwara-Vergne groups
Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson
In 2017 Bar-Natan and the first author showed that solutions to the Kashiwara--Vergne equations are in bijection with certain knot invariants: homomorphic expansions of welded foam…
Circuit algebras are wheeled props
Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams"…
An infinity operad of normalized cacti
Luciana Basualdo Bonatto, Safia Chettih, Abigail Linton +3
We show that normalized cacti form an -operad in the form of a dendroidal space satisfying a weak Segal condition. To do this, we introduce a new topological operad of brac…
Modular operads and the nerve theorem
Philip Hackney, Marcy Robertson, Donald Yau
We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modula…
A graphical category for higher modular operads
Philip Hackney, Marcy Robertson, Donald Yau
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Qui…
On factorizations of graphical maps
Philip Hackney, Marcy Robertson, Donald Yau
We study the categories governing infinity (wheeled) properads. The graphical category, which was already known to be generalized Reedy, is in fact an Eilenberg-Zilber category. A…
Operads of genus zero curves and the Grothendieck-Teichmüller group
Pedro Boavida de Brito, Geoffroy Horel, Marcy Robertson
We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichmüller group. Using…
Lecture notes on infinity-properads
Philip Hackney, Marcy Robertson
These are notes for three lectures on higher properads given at a program at the mathematical institute MATRIX in Australia in June 2016. The first lecture covers the case of opera…
Higher cyclic operads
Philip Hackney, Marcy Robertson, Donald Yau
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which…
Shrinkability, relative left properness, and derived base change
Philip Hackney, Marcy Robertson, Donald Yau
For a connected pasting scheme , under reasonable assumptions on the underlying category, the category of -colored -props admits a cofibrantly…
A simplicial model for infinity properads
Philip Hackney, Marcy Robertson, Donald Yau
We show how the model structure on the category of simplicially-enriched (colored) props induces a model structure on the category of simplicially-enriched (colored) properads. A s…
Relative left properness of colored operads
Philip Hackney, Marcy Robertson, Donald Yau
The category of -colored symmetric operads admits a cofibrantly generated model category structure. In this paper, we show that this model structure satisfies a relat…
Infinity Properads and Infinity Wheeled Properads
Philip Hackney, Marcy Robertson, Donald Yau
A theory of -properads is developed, extending both the Joyal-Lurie -categories and the Cisinski-Moerdijk-Weiss -operads. Every connected wheel-free graph g…
Representations of derived A-infinity algebras
Camil I. Aponte Roman, Muriel Livernet, Marcy Robertson +2
The notion of a derived A-infinity algebra arose in the work of Sagave as a natural generalisation of the classical A-infinity algebra, relevant to the case where one works over a…
Cluster categories for topologists
Julia E. Bergner, Marcy Robertson
We consider triangulated orbit categories, with the motivating example of cluster categories, in their usual context of algebraic triangulated categories, then present them from an…
The homotopy theory of simplicial props
Philip Hackney, Marcy Robertson
The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher…
On the category of props
Philip Hackney, Marcy Robertson
The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties:…
The Homotopy Theory of Simplicially Enriched Multicategories
Marcy Robertson
In this paper we construct a cofibrantly generated model category structure on the category of all small symmetric multicategories enriched in simplicial sets.
Spaces of Operad Structures
Marcy Robertson
The purpose of this paper is to study the derived category of simplicial multicategories with arbitrary sets of objects (also known as, colored operads in simplicial sets). Our mai…