2,398 research outputs found
Smoothing finite group actions on three-manifolds
We show that every continuous action of a finite group on a smooth
three-manifold is a uniform limit of smooth actions.Comment: Final version to appear in Duke Math Journal, 34 pages, 2 figure
The Hilbert--Smith conjecture for three-manifolds
We show that every locally compact group which acts faithfully on a connected
three-manifold is a Lie group. By known reductions, it suffices to show that
there is no faithful action of (the -adic integers) on a
connected three-manifold. If acts faithfully on , we find an
interesting -invariant open set with
and analyze the incompressible surfaces in representing
a generator of . It turns out that there must be one such
incompressible surface, say , whose isotopy class is fixed by .
An analysis of the resulting homomorphism
gives the desired contradiction. The approach is local on .Comment: 24 pages, 1 figure; to appear in Journal of the AM
Central limit theorems for random polygons in an arbitrary convex set
We study the probability distribution of the area and the number of vertices
of random polygons in a convex set . The novel aspect of
our approach is that it yields uniform estimates for all convex sets
without imposing any regularity conditions on the
boundary . Our main result is a central limit theorem for both the
area and the number of vertices, settling a well-known conjecture in the field.
We also obtain asymptotic results relating the growth of the expectation and
variance of these two functionals.Comment: Published in at http://dx.doi.org/10.1214/10-AOP568 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Gradients in abundance and diversity of ground-dwelling arthropods in temperate silvoarable fields
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Algebraic varieties with semialgebraic universal cover
We study projective varieties whose universal cover is biholomorphic to a
semialgebraic open subset of a projective variety
On the distortion of knots on embedded surfaces
Our main result is a nontrivial lower bound for the distortion of some
specific knots. In particular, we show that the distortion of the torus knot
satisfies . This answers a
1983 question of Gromov
Sectorial descent for wrapped Fukaya categories
We develop a set of tools for doing computations in and of (partially)
wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf)
property for the wrapped Fukaya category with respect to so-called Weinstein
sectorial coverings and (2) that the partially wrapped Fukaya category of a
Weinstein manifold with respect to a mostly Legendrian stop is generated by the
cocores of the critical handles and the linking disks to the stop. We also
prove (3) a `stop removal equals localization' result, and (4) that the
Fukaya--Seidel category of a Lefschetz fibration with Weinstein fiber is
generated by the Lefschetz thimbles. These results are derived from three main
ingredients, also of independent use: (5) a K\"unneth formula (6) an exact
triangle in the Fukaya category associated to wrapping a Lagrangian through a
Legendrian stop at infinity and (7) a geometric criterion for when a
pushforward functor between wrapped Fukaya categories of Liouville sectors is
fully faithful.Comment: 111 pages, 29 figure
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