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Journals and Conferences
We compute an invariant counting gradient flow lines (including closed orbits) in S-valued Morse theory, and relate it to Reidemeister torsion for manifolds with χ = 0, b1 > 0. Here we extend the results in  following a different approach. However, this paper is written in a self-contained manner and may be read independently of . The motivation of… (More)
In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory invariant is a topological invariant. It is hoped that this will provide a model for possible generalizations to Floer… (More)
Let be a surface with a symplectic form, let φ be a symplectomorphism of , and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in R×Y , with cylindrical ends asymptotic to periodic orbits of φ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some… (More)
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology of certain Legendrian tori in fivedimensional contact manifolds. We present several computations and… (More)
We characterize least-perimeter enclosures of prescribed area on some piecewise smooth manifolds, including certain polyhedra, double spherical caps, and cylindrical cans. 2000 Mathematics subject classification: primary 49Q10, 53A10.
As in the United States, increased concentration in grocery retailing in Great Britain has raised issues about the buying power of multiple retailers. Whether, and if so how, it prevents, restricts, or distorts competition at the retail and/or producer level to the public or consumer detriment has been the central aspect of concern in a number of formal… (More)
We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected 3-manifold with a stable Hamiltonian structure, and let R denote the associated Reeb vector field on Y . We prove that if Y is not a T2 -bundle over S1 , then R has… (More)
The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2π/3.
We prove necessary and sufficient conditions for an arbitrary invariant of braids with m double points to be the “mth derivative” of a braid invariant. We show that the “primary obstruction to integration” is the only obstruction. This gives a slight generalization of the existence theorem for Vassiliev invariants of braids. We give a direct proof by… (More)
We prove that the least-perimeter way to enclose prescribed area in the plane with smooth, rotationally symmetric, complete metric of nonincreasing Gauss curvature consists of one or two circles, bounding a disc, the complement of a disc, or an annulus. We also provide a new isoperimetric inequality in general surfaces with boundary.