59 research outputs found
Hypercommutative operad as a homotopy quotient of BV
We give an explicit formula for a quasi-isomorphism between the operads
Hycomm (the homology of the moduli space of stable genus 0 curves) and
BV/ (the homotopy quotient of Batalin-Vilkovisky operad by the
BV-operator). In other words we derive an equivalence of Hycomm-algebras and
BV-algebras enhanced with a homotopy that trivializes the BV-operator.
These formulas are given in terms of the Givental graphs, and are proved in
two different ways. One proof uses the Givental group action, and the other
proof goes through a chain of explicit formulas on resolutions of Hycomm and
BV. The second approach gives, in particular, a homological explanation of the
Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
Derived coisotropic structures II: stacks and quantization
We extend results about -shifted coisotropic structures from part I of
this work to the setting of derived Artin stacks. We show that an intersection
of coisotropic morphisms carries a Poisson structure of shift one less. We also
compare non-degenerate shifted coisotropic structures and shifted Lagrangian
structures and show that there is a natural equivalence between the two spaces
in agreement with the classical result. Finally, we define quantizations of
-shifted coisotropic structures and show that they exist for .Comment: 45 pages. Contains the second half of arXiv:1608.01482v1 with new
material adde
Notes on factorization algebras, factorization homology and applications
These notes are an expanded version of two series of lectures given at the
winter school in mathematical physics at les Houches and at the Vietnamese
Institute for Mathematical Sciences. They are an introduction to factorization
algebras, factorization homology and some of their applications, notably for
studying -algebras. We give an account of homology theory for manifolds
(and spaces), which give invariant of manifolds but also invariant of
-algebras. We particularly emphasize the point of view of factorization
algebras (a structure originating from quantum field theory) which plays, with
respect to homology theory for manifolds, the role of sheaves with respect to
singular cohomology. We mention some applications to the study of mapping
spaces and study several examples, including some over stratified spaces.Comment: 122 pages. A few examples adde
Melatonin and cancer risk: does light at night compromise physiologic cancer protection by lowering serum melatonin levels?
Effects of Prior Exposure to Prolonged Continuous Light on the Pattern of Melatonin Secretion in Sheep Held Under Continuous Darkness
Convergence of biorthogonal series of biharmonic eigenfunctions by the method of titchmarsh
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