8,120 research outputs found
Wheeled PROPs, graph complexes and the master equation
We introduce and study wheeled PROPs, an extension of the theory of PROPs
which can treat traces and, in particular, solutions to the master equations
which involve divergence operators. We construct a dg free wheeled PROP whose
representations are in one-to-one correspondence with formal germs of
SP-manifolds, key geometric objects in the theory of Batalin-Vilkovisky
quantization. We also construct minimal wheeled resolutions of classical
operads Com and Ass as rather non-obvious extensions of Com_infty and
Ass_infty, involving, e.g., a mysterious mixture of associahedra with
cyclohedra. Finally, we apply the above results to a computation of cohomology
of a directed version of Kontsevich's complex of ribbon graphs.Comment: LaTeX2e, 63 pages; Theorem 4.2.5 on bar-cobar construction is
strengthene
Split Grothendieck rings of rooted trees and skew shapes via monoid representations
We study commutative ring structures on the integral span of rooted trees and
-dimensional skew shapes. The multiplication in these rings arises from the
smash product operation on monoid representations in pointed sets. We interpret
these as Grothendieck rings of indecomposable monoid representations over
\fun - the "field" of one element. We also study the base-change homomorphism
from \mt-modules to -modules for a field containing all roots of
unity, and interpret the result in terms of Jordan decompositions of adjacency
matrices of certain graphs.Comment: arXiv admin note: text overlap with arXiv:1706.0390
Maurer-Cartan Elements and Cyclic Operads
First we argue that many BV and homotopy BV structures, including both
familiar and new examples, arise from a common underlying construction. The
input of this construction is a cyclic operad along with a cyclically invariant
Maurer-Cartan element in an associated Lie algebra. Using this result we
introduce and study the operad of cyclically invariant operations, with
instances arising in cyclic cohomology and equivariant homology. We
compute the homology of the cyclically invariant operations; the result being
the homology operad of , the uncompactified moduli spaces
of punctured Riemann spheres, which we call the gravity operad after Getzler.
Motivated by the line of inquiry of Deligne's conjecture we construct `cyclic
brace operations' inducing the gravity relations up-to-homotopy on the cochain
level. Motivated by string topology, we show such a gravity-BV pair is related
by a long exact sequence. Examples and implications are discussed in course.Comment: revised version to appear in the Journal of Noncommutative Geometr
Aircraft vortex marking program
A simple, reliable device for identifying atmospheric vortices, principally as generated by in-flight aircraft and with emphasis on the use of nonpolluting aerosols for marking by injection into such vortex (-ices) is presented. The refractive index and droplet size were determined from an analysis of aerosol optical and transport properties as the most significant parameters in effecting vortex optimum light scattering (for visual sighting) and visual persistency of at least 300 sec. The analysis also showed that a steam-ejected tetraethylene glycol aerosol with droplet size near 1 micron and refractive index of approximately 1.45 could be a promising candidate for vortex marking. A marking aerosol was successfully generated with the steam-tetraethylene glycol mixture from breadboard system hardware. A compact 25 lb/f thrust (nominal) H2O2 rocket chamber was the key component of the system which produced the required steam by catalytic decomposition of the supplied H2O2
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