arXiv subjects

Baptiste Gros

Publications and source records attributed to Baptiste Gros.

3 recordsLinked to original sources

arXiv2025

Strong Geometry : Knots

In this paper, we introduce the notion of strong geometry, a structure composed by both the chirotope of a set of points X in the d-dimensional space and the wedge chirotope which is the specific adjoint chirotope induced by the hyperplanes spanned by X. We present various properties relating these two chirotopes, for instance, by introducing the witness chirotope, we are able to give a formula expressing the wedge chirotope in terms of the usual chirotope. With this on hand, we answer positively a strong geometry version of a question due to M. Las Vergnas about reconstructing polygonal knots via chirotopes. Moreover, we also show that linear spatial graphs are determined by their corresponding strong geometries.

math.CO↗

arXiv2024

Computing the determinant of links through Fourier-Hadamard transforms

In this paper, we present a novel method to compute the determinant of a link using Fourier-Hadamard transforms of Boolean functions. We also investigate the determinant of centrally symmetric links (a special class of strong achiral links). In particular, we show that the determinant of a centrally symmetric link with an even number of components is equals zero.

math.GT↗

arXiv2022

A combinatorial one-cocycle in a moduli space of knots from the Vassiliev invariant of order 3

The theory of Gauss diagrams and Gauss diagram formulas provides convenient ways to compute knot invariants, such as coefficients of the HOMFLYPT polynomial. In \cite{4,5}, the author uses Gauss diagram formulas to find combinatorial 1-cocycles in the moduli space of knots in the solid torus. Evaluated on canonical loops, one can then obtain new, non trivial knot invariants. In those books, the author conjectures that a new formula, based on the Vassiliev invariant $v_3$ also gives a 1-cocycle. We prove that it is in fact true by using the same methods developed by the author in those books.

math.GT↗