Spencer Cattalani

activity

20222025

collaborators

7 papers

math.SG2025

On Gromov Width under $C^{0}$ Deformations

Spencer Cattalani

We construct a uniformly bounded symplectic structure on $S^{2} \times R^{4}$ admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conje…

math.SG2025

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…

math.MG2025

Smooth Approximations of Quasispheres

Spencer Cattalani

We prove that every $n$ -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…

math.DG2024

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 $4$ . In particular, we show that, for $n \leq 4$ , a polyhedral $n$ -manifold…

math.SG2024

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…

math.SG2023

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…

On Gromov Width under C0 Deformations

Ahlfors Currents and Symplectic Non-Hyperbolicity

Smooth Approximations of Quasispheres

Quantitative Smoothing of Polyhedral Manifolds

Positivity of Intersections and Tameness of Almost Complex 4-manifolds

Coarsely Holomorphic Curves and Symplectic Topology

On Gromov Width under $C^{0}$ Deformations