5,675 research outputs found
Swiss-Cheese operad and Drinfeld center
We build a model in groupoids for the Swiss-Cheese operad, based on
parenthesized permutations and braids, and we relate algebras over this model
to the classical description of algebras over the homology of the Swiss-Cheese
operad. We extend our model to a rational model for the Swiss-Cheese operad,
and we compare it to the model that we would get if the operad Swiss-Cheese
were formal.Comment: 27 pages. v5: Minor corrections. To appear in Israel J. Mat
Formality of a higher-codimensional Swiss-Cheese operad
We study configurations of points in the complement of a linear subspace
inside a Euclidean space, with . We define a higher-codimensional Swiss-Cheese operad
associated to such configurations, a variant of the
classical Swiss-Cheese operad. The operad is weakly
equivalent to the operad of locally constant factorization algebras on the
stratified space . We prove that
this operad is formal over .Comment: 50 pages, comments welcome. v2: Added two appendices and corrected
Section 5.
The Lambrechts-Stanley Model of Configuration Spaces
We prove the validity over of a commutative differential graded
algebra model of configuration spaces for simply connected closed smooth
manifolds, answering a conjecture of Lambrechts--Stanley. We get as a result
that the real homotopy type of such configuration spaces only depends on the
real homotopy type of the manifold. We moreover prove, if the dimension of the
manifold is at least , that our model is compatible with the action of the
Fulton--MacPherson operad (weakly equivalent to the little disks operad) when
the manifold is framed. We use this more precise result to get a complex
computing factorization homology of framed manifolds. Our proofs use the same
ideas as Kontsevich's proof of the formality of the little disks operads.Comment: 61 pages. To appear in Inventiones Mathematica
Configuration Spaces of Manifolds with Boundary
We study ordered configuration spaces of compact manifolds with boundary. We
show that for a large class of such manifolds, the real homotopy type of the
configuration spaces only depends on the real homotopy type of the pair
consisting of the manifold and its boundary. We moreover describe explicit real
models of these configuration spaces using three different approaches. We do
this by adapting previous constructions for configuration spaces of closed
manifolds which relied on Kontsevich's proof of the formality of the little
disks operads. We also prove that our models are compatible with the richer
structure of configuration spaces, respectively a module over the Swiss-Cheese
operad, a module over the associative algebra of configurations in a collar
around the boundary of the manifold, and a module over the little disks operad.Comment: 107 page
Dynamical patterns of human postural responses to emotional stimuli
Erotic scenes and images of mutilated bodies are emotional stimuli that have repeatedly shown to evoke specific neurophysiological responses associated with enhanced attention and perceptual processing. Remarkably however, only a handful of studies have investigated human motor reactions to emotional activation as a direct index of physical approximation or withdrawal. Given the inconclusive results of these studies, the approach-avoidance distinction, one of the most salient concepts in human motivational research, remains a broadly exploited hypothesis that has never been empirically demonstrated. Here, we investigate postural responses elicited by discrete emotional stimuli in healthy young adults. We discover that both positive and negative affective pictures induce a significant posterior deviation from postural baseline equilibrium. Further, we find that neutral pictures also evoke posterior deviation, although with a less pronounced amplitude. Exploring the dynamical evolution of postural responses to emotional pictures at high temporal resolution, we uncover a characteristic profile that remains stable for stimuli from all three affective categories. In contrast, the postural response amplitude is modulated by the emotional content of the stimulus. Our observations do not support the interpretation of postural responses to affective picture-viewing as approach-avoidance behavior. Instead, our findings indicate the involvement of a previously unrecognized motor component of the physiological mechanism underlying human orienting responses
- …