605 research outputs found
Character formulas for the operad of two compatible brackets and for the bihamiltonian operad
We compute dimensions of the components for the operad of two compatible
brackets and for the bihamiltonian operad. We also obtain character formulas
for the representations of the symmetric groups and the group in these
spaces.Comment: 24 pages, accepted by Functional Analysis and its Applications, a few
typos correcte
The homotopy theory of simplicial props
The category of (colored) props is an enhancement of the category of colored
operads, and thus of the category of small categories. In this paper, the
second in a series on "higher props," we show that the category of all small
colored simplicial props admits a cofibrantly generated model category
structure. With this model structure, the forgetful functor from props to
operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat
The significance of the amorphous potential energy landscape for dictating glassy dynamics and driving solid-state crystallisation
Contains fulltext :
180674.pdf (publisher's version ) (Open Access
Quantum Open-Closed Homotopy Algebra and String Field Theory
We reformulate the algebraic structure of Zwiebach's quantum open-closed
string field theory in terms of homotopy algebras. We call it the quantum
open-closed homotopy algebra (QOCHA) which is the generalization of the
open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy
formulation reveals new insights about deformations of open string field theory
by closed string backgrounds. In particular, deformations by Maurer Cartan
elements of the quantum closed homotopy algebra define consistent quantum open
string field theories.Comment: 36 pages, fixed typos and small clarifications adde
The structure of 2D semi-simple field theories
I classify all cohomological 2D field theories based on a semi-simple complex
Frobenius algebra A. They are controlled by a linear combination of
kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their
effect on the Gromov-Witten potential is described by Givental's Fock space
formulae. This leads to the reconstruction of Gromov-Witten invariants from the
quantum cup-product at a single semi-simple point and from the first Chern
class, confirming Givental's higher-genus reconstruction conjecture. The proof
uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio
Aortic dissection: visualisation of aortic blood flow and quantification of wall shear stress using time-resolved, 3D phase-contrast MRI
Curved Koszul duality theory
38 pagesInternational audienceWe extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the category of coproperads to include objects endowed with a curvature. As usual, the bar-cobar construction gives a (large) cofibrant resolution for any properad, such as the properad encoding unital and counital Frobenius algebras, a notion which appears in 2d-TQFT. We also define a curved Koszul duality theory for operads or properads presented with quadratic, linear and constant relations, which provides the possibility for smaller relations. We apply this new theory to study the homotopy theory and the cohomology theory of unital associative algebras
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