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, $\mathbb{R}^{n} \setminus \mathbb{R}^{m}$ with $n - m \ge 2$. We define a higher-codimensional Swiss-Cheese operad $\mathsf{VSC}_{mn}$ associated to such configurations, a variant of the classical Swiss-Cheese operad. The operad $\mathsf{VSC}_{mn}$ is weakly equivalent to the operad of locally constant factorization algebras on the stratified space $\{\mathbb{R}^{m} \subset \mathbb{R}^{n}\}$. We prove that this operad is formal over $\mathbb{R}$.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 $\mathbb{R}$ 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 $4$, 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