Related papers: Higher Homotopy Operations
This is the first in a sequence of articles exploring the relationship between commutative algebras and $E_\infty$-algebras in characteristic $p$ and mixed characteristic. In this paper we lay the groundwork by defining a new class of…
We give a particular choice of the higher Eilenberg-MacLane maps by a recursive formula.This choice leads to a simple description of the homotopy operations for simplicial Z/2-algebras.
The notion of a \emph{higher-order algebroid}, as introduced by J\'o\'zwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the concepts of a…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
We characterise the set of fundamental groups for which there exist $n$-manifolds that are $h$-cobordant (hence homotopy equivalent) but not simple homotopy equivalent, when $n$ is sufficiently large. In particular, for $n \ge 12$ even, we…
Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…
Higher homotopies are nowadays playing a prominent role in mathematics as well as in certain branches of theoretical physics. We recall some of the connections between the past and the present developments. Higher homotopies were isolated…
This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_\infty$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence,…
Examples of non-trivial higher string topology operations have been regrettably rare in the literature. In this paper, working in the context of string topology of classifying spaces, we provide explicit calculations of a wealth of…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
Higher order group cohomology is defined and first properties are given. Using modular symbols, an Eichler-Shimura homomorphism is constructed mapping spaces of higher order cusp forms to higher order cohomology groups.
This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also…
Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…
We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad with comultiplication induces a homology theory that is…
We are studying here a family of probability density functions indexed by a real parameter, and constructed from homographic relations between associated Stieltjes transforms. From the analysis of orthogonal polynomials we deduce a family…
We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…
In this paper, I introduce a new generalization of the concept of an operad, further generalizing the concept of an opetope introduced by Baez and Dolan, who used this for the definition of their version of non-strict $n$-categories.…
The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the…