456 research outputs found
The Transfer is Functorial
We prove that the Becker-Gottlieb transfer is functorial up to homotopy, for
all fibrations with finitely dominated fibers. This resolves a lingering
foundational question about the transfer, which was originally defined in the
late 1970s in order to simplify the proof of the Adams conjecture. Our approach
differs from previous attempts in that we closely emulate the geometric
argument in the case of a smooth fiber bundle. This leads to a
"multiplicative'" description of the transfer, different from the standard
presentation as the trace of a diagonal map.Comment: This is the final preprint version. The article is to appear in the
Advances in Mathematic
Origin and reduction of wakefields in photonic crystal accelerator cavities
Photonic crystal (PhC) defect cavities that support an accelerating mode tend
to trap unwanted higher-order modes (HOMs) corresponding to zero-group-velocity
PhC lattice modes at the top of the bandgap. The effect is explained quite
generally from photonic band and perturbation theoretical arguments. Transverse
wakefields resulting from this effect are observed in a hybrid dielectric PhC
accelerating cavity based on a triangular lattice of sapphire rods. These
wakefields are, on average, an order of magnitude higher than those in the
waveguide-damped Compact Linear Collider (CLIC) copper cavities. The avoidance
of translational symmetry (and, thus, the bandgap concept) can dramatically
improve HOM damping in PhC-based structures.Comment: 11 pages, 18 figures, 2 table
On the multiplicativity of the Euler characteristic
In this short paper, we give two proofs that the Euler characteristic is
multiplicative, for fiber sequences of finitely dominated spaces. This is
equivalent to proving that the Becker-Gottlieb transfer is functorial on
.Comment: Accepted version. 13 pages plus reference
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