1,141 research outputs found
Compactness for Holomorphic Supercurves
We study the compactness problem for moduli spaces of holomorphic supercurves
which, being motivated by supergeometry, are perturbed such as to allow for
transversality. We give an explicit construction of limiting objects for
sequences of holomorphic supercurves and prove that, in important cases, every
such sequence has a convergent subsequence provided that a suitable extension
of the classical energy is uniformly bounded. This is a version of Gromov
compactness. Finally, we introduce a topology on the moduli spaces enlarged by
the limiting objects which makes these spaces compact and metrisable.Comment: 38 page
Removal of singularities and Gromov compactness for symplectic vortices
We prove that the moduli space of gauge equivalence classes of symplectic
vortices with uniformly bounded energy in a compact Hamiltonian manifold admits
a Gromov compactification by polystable vortices. This extends results of
Mundet i Riera and Tian for circle actions to the case of arbitrary compact Lie
groups. Our argument relies on an a priori estimate for vortices that allows us
to apply techniques used by McDuff and Salamon in their proof of Gromov
compactness for pseudoholomorphic curves. As an intermediate result we prove a
removable singularity theorem for vortices.Comment: Minor changes and correction
Morse homology for the heat flow
We use the heat flow on the loop space of a closed Riemannian manifold to
construct an algebraic chain complex. The chain groups are generated by
perturbed closed geodesics. The boundary operator is defined in the spirit of
Floer theory by counting, modulo time shift, heat flow trajectories that
converge asymptotically to nondegenerate closed geodesics of Morse index
difference one.Comment: 89 pages, 3 figure
Weighted Dirac combs with pure point diffraction
A class of translation bounded complex measures, which have the form of
weighted Dirac combs, on locally compact Abelian groups is investigated. Given
such a Dirac comb, we are interested in its diffraction spectrum which emerges
as the Fourier transform of the autocorrelation measure. We present a
sufficient set of conditions to ensure that the diffraction measure is a pure
point measure. Simultaneously, we establish a natural link to the theory of the
cut and project formalism and to the theory of almost periodic measures. Our
conditions are general enough to cover the known theory of model sets, but also
to include examples such as the visible lattice points.Comment: 44 pages; several corrections and improvement
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