600 research outputs found
Legendrian contact homology in
This is an introduction to Legendrian contact homology and the
Chekanov-Eliashberg differential graded algebra, with a focus on the setting of
Legendrian knots in .Comment: v3: 59 pages, 27 figures; introduction rewritten, sections 5 and 6
switched, many small revision
Lagrangian Cobordisms via Generating Families: Constructions and Geography
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced
from isotopy, spinning, and handle attachment constructions that employ the
technique of generating families. Moreover, any Legendrian with a generating
family has an immersed Lagrangian filling with a compatible generating family.
These constructions are applied in several directions, in particular to a
non-classical geography question: any graded group satisfying a duality
condition can be realized as the generating family homology of a connected
Legendrian submanifold in R^{2n+1} or in the 1-jet space of any compact
n-manifold with n at least 2.Comment: 34 pages, 11 figures. v2: corrected a referenc
Tame stacks in positive characteristic
We introduce and study a class of algebraic stacks with finite inertia in
positive and mixed characteristic, which we call tame algebraic stacks. They
include tame Deligne-Mumford stacks, and are arguably better behaved than
general Deligne-Mumford stacks. We also give a complete characterization of
finite flat linearly reductive schemes over an arbitrary base. Our main result
is that tame algebraic stacks are \'etale locally quotient by actions of
linearly reductive finite group schemes.
In a subsequent paper we will show that tame algebraic stacks admit a good
theory of stable maps.Comment: 31 pages, 3 sections and 1 appendi
Contact Structures on Plumbed 3-Manifolds
In this paper, we show that the Ozsv\'ath-Szab\'o contact invariant
of a contact 3-manifold can be calculated
combinatorially if is the boundary of a certain type of plumbing , and
is induced by a Stein structure on . Our technique uses an algorithm
of Ozsv\'ath and Szab\'o to determine the Heegaard-Floer homology of such
3-manifolds. We discuss two important applications of this technique in contact
topology. First, we show that it simplifies the calculation of the
Ozsv\'ath-Stipsicz-Szab\'o obstruction to admitting a planar open book. Then we
define a numerical invariant of contact manifolds that respects a partial
ordering induced by Stein cobordisms. We do a sample calculation showing that
the invariant can get infinitely many distinct values.Comment: Added some examples and comment
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