362 research outputs found
Lagrangian caps
We establish an -principle for exact Lagrangian embeddings with concave
Legendrian boundary. We prove, in particular, that in the complement of the
unit ball in the standard symplectic , there exists an
embedded Lagrangian -disc transversely attached to along its Legendrian
boundary.Comment: 38 pages, 6 figure
Amenable groups and smooth topology of 4-manifolds
A smooth five-dimensional s-cobordism becomes a smooth product if stabilized
by a finite number n of 's. We show that for amenable
fundamental groups, the minimal n is subextensive in covers, i.e.,
n(cover)/index(cover) has limit 0. We focus on the notion of sweepout width,
which is a bridge between 4-dimensional topology and coarse geometry
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