Results 51 to 60 of about 3,791 (108)
Steenrod operations via higher Bruhat orders
Proceedings of the London Mathematical Society, Volume 130, Issue 2, February 2025.Abstract The purpose of this paper is to establish a correspondence between the higher Bruhat orders of Yu. I. Manin and V. Schechtman, and the cup‐i$i$ coproducts defining Steenrod squares in cohomology. To any element of the higher Bruhat orders, we associate a coproduct, recovering Steenrod's original ones from extremal elements in these orders ...
Guillaume Laplante‐Anfossi +1 more
wiley +1 more source
Quillen homology for operads via Gr\"obner bases [PDF]
, 2013 The main goal of this paper is to present a way to compute Quillen homology of operads. The key idea is to use the notion of a shuffle operad we introduced earlier; this allows to compute, for a symmetric operad, the homology classes and the shape of the
Dotsenko, Vladimir, Khoroshkin, Anton
core +1 more source
On the equivalence of Lurie's ∞$\infty$‐operads and dendroidal ∞$\infty$‐operads
Journal of Topology, Volume 17, Issue 4, December 2024.Abstract In this paper, we prove the equivalence of two symmetric monoidal ∞$\infty$‐categories of ∞$\infty$‐operads, the one defined in Lurie [Higher algebra, available at the author's homepage, http://math.ias.edu/~lurie/, September 2017 version] and the one based on dendroidal spaces.
Vladimir Hinich, Ieke Moerdijk
wiley +1 more source
Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds
Journal of Topology, Volume 17, Issue 1, March 2024.Abstract We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds Ug,1n:=#g(Sn×Sn+1)∖int(D2n+1)$U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}(D^{2n+1})$, for large g$g$ and n$n$, up to degree n−3$n-3$.
Johannes Ebert, Jens Reinhold
wiley +1 more source
What is an equivalence in a higher category?
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 1-58, January 2024.Abstract The purpose of this survey is to present in a uniform way the notion of equivalence between strict n$n$‐categories or (∞,n)$(\infty ,n)$‐categories, and inside a strict (n+1)$(n+1)$‐category or (∞,n+1)$(\infty ,n+1)$‐category.
Viktoriya Ozornova, Martina Rovelli
wiley +1 more source
Noncommutative calculus and operads [PDF]
, 2012 This is a survey of current and recent works on deformation quantization and index ...
Tsygan, Boris
core
Curved infinity-algebras and their characteristic classes
, 2012 In this paper we study a natural extension of Kontsevich's characteristic class construction for A-infinity and L-infinity algebras to the case of curved algebras.
Lazarev, Andrey, Schedler, Travis
core +1 more source
Algebras of higher operads as enriched categories II
, 2009 66 pages. In version 2 we corrected the explicit construction of coequalisers in categories of algebras from section 7 of version 1. The new appendices discuss the background on these transfinite constructions more fully.
Batanin, Michael +2 more
openaire +2 more sources
On several varieties of cacti and their relations
, 2005 Motivated by string topology and the arc operad, we introduce the notion of quasi-operads and consider four (quasi)-operads which are different varieties of the operad of cacti.
Kassel, Penner, Ralph M Kaufmann
core +1 more source
The Combinatorics of Iterated Loop Spaces
, 2003 It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads.
Batanin, M. A.
core +1 more source