A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New stabilization methods for exotic surfaces in 4-manifolds.
New mapping classes of knotted surfaces are computed via surgery.
Computes extendable mapping classes for knotted surfaces in .
In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold while leaving the topological embedding unchanged.
Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we constr…
We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic…
New surfaces in 4-ball differ topologically but not diffeomorphically.
In this paper, given a knot K, for any integer m we construct a new surface Sigma_K(m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the `rim surgery' which was introduced by Fintushel and Stern, by doing additional twist spi…
Surface corks modify 4-manifold structures without changing their homeomorphism type.