1 citations · 1 across the 8 of their papers we have counts for
8 papers
On Gromov Width under Deformations
Spencer Cattalani
We construct a uniformly bounded symplectic structure on admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conje…
Ahlfors Currents and Symplectic Non-Hyperbolicity
Spencer Cattalani
Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. Inspired by Duval's work on Ahlfors currents, we use t…
Smooth Approximations of Quasispheres
Spencer Cattalani
We prove that every -dimensional quasisphere is the Gromov-Hausdorff limit of a sequence of locally smooth uniform quasispheres. We also prove an analogous result in the bi-Lips…
Quantitative Smoothing of Polyhedral Manifolds
Spencer Cattalani
We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most . In particular, we show that, for , a polyhedral -manifold…
Positivity of Intersections and Tameness of Almost Complex 4-manifolds
Spencer Cattalani
We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almo…
Coarsely Holomorphic Curves and Symplectic Topology
Spencer Cattalani
A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost c…
Verifying the Hilali conjecture up to formal dimension twenty
Spencer Cattalani, Aleksandar Milivojević
We prove that in formal dimension the Hilali conjecture holds, i.e. that the total dimension of the rational homology bounds from above the total dimension of the rationa…
Pseudocycles for Borel-Moore Homology
Spencer Cattalani, Aleksey Zinger
Pseudocycles are geometric representatives for integral homology classes on smooth manifolds that have proved useful in particular for defining gauge-theoretic invariants. The Bore…