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.
Characterizes null Lagrangians in Cosserat elasticity.
Null Lagrangian-preserving surgeries are a generalization of the Garoufalidis and Rozansky null-moves, that these authors introduced to study the Kricker lift of the Kontsevich integral, in the setting of pairs (M,K) composed of a rational homology sphere M and a null-homologous knot K in M. They are defined as replace…
Researchers prove a generalized Piola identity for Riemannian manifolds.
New proof of isoperimetric inequality using integration by parts.
Kricker defined an invariant of knots in homology 3-spheres which is a rational lift of the Kontsevich integral, and proved with Garoufalidis that this invariant satisfies splitting formulas with respect to a surgery move called null-move. We define a functorial extension of the Kricker invariant and prove splitting fo…
In a previous article, we constructed an invariant Z for null-homologous knots in rational homology spheres, from equivariant intersections in configuration spaces. Here we present an equivalent definition of Z in terms of configuration space integrals, we prove that Z is multiplicative under connected sum, and we prov…
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for knots in integral homology 3-spheres. We give a partial combinatorial …
In the setting of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries, there are two candidates to be universal invariants, defined respectively by Kricker and Lescop. In a previous paper, the second author defined maps between spaces of J…
New calibration energy measures deviation from calibrated geometry, enabling mean curvature flow in infinite volumes.
Given a null-homologous knot in a rational homology 3-sphere , and the standard infinite cyclic covering of , we define an invariant of triples of curves in , by means of equivariant triple intersections of surfaces. We prove that this invariant provides a map on $\Al^{\otimes 3…