Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies, to automatic detection of network dynamics, to understanding the neural representation of natural auditory signals, and to demonstrating that the population activity of grid cells...
The usual Swiss-Cheese operad encodes triplets (A,B,f), where A is an algebra over the little disks operad in dimension n (i.e., an \mathsf{E}n-algebra), B is an \mathsf{E}{n-1}-algebra, and f : A \to Z(B) is a central morphism of E_n-algebras.
The Swiss-Cheese operad admits several variants and generalizations. In Voronov's original version, the morphism is replaced by an action A...
Over the past decade, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies, to automatic detection of network dynamics, to understanding the neural representation of natural auditory signals, and to demonstrating that the population activity of grid cells...
Nous présentons une nouvelle famille de réalisations des opéraèdres, une famille de polytopes qui codent les opérades à homotopie près comprenant l'associaèdre et le permutoèdre. En se servant des techniques récemment développées par N. Masuda, A. Tonks, H. Thomas et B. Vallette, nous définissons une approximation cellulaire de la diagonale pour cette famille de polytopes de même que le...
Crossed modules are algebraic models of homotopy 2-types and hence have \pi_1 and \pi_2 . We propose a definition of the centre of a crossed module whose essential invariants can be computed via the group cohomology H^i (\pi_1, \pi_2). This definition therefore has much nicer properties than one proposed by Norrie in the 80’s.
Model categories give an abstract setting for homotopy theory, allowing study of different notions of equivalence. I'll discuss various categories with associated functorial spectral sequences. In such settings, one can consider a hierarchy of notions of equivalence, given by morphisms inducing an isomorphism at a fixed stage of the associated spectral sequence. I'll discuss model structures...
