Search results for "invariants"

A note on rank 2 diagonals

2020

<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>

Voisinages tubulaires épointés et homotopie stable à l'infini

2022

We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…

Equivalence relations among homology 3-spheres and the Johnson filtration

2021

The Torelli group of a surface consists of isotopy classes of homeomorphisms of this surface acting trivially at the homological level. The structure of the Torelli group can be approached by the study and the comparison of two filtrations of this group: its lower central series, and the "Johnson" filtration, given by the kernels of the natural actions on the successive nilpotent quotients of the fundamental group of the surface. It is now known that there are, via the notion of "Heegaard splittings", rich interactions between this 2-dimensional study and the study of some 3-manifolds topological invariants: we refer here precisely to the so-called "finite-type" invariants. In this PhD, we …

A closed formula for the evaluation of foams

2020

International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homology categorifying the sl(N) link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.

ALGEBRE SIMMETRICHE DI ALCUNE CLASSI DI IDEALI MONOMIALI

The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting class of monomial ideals: the ideals L ⊂S=K[x1,...,xn,y1,...,ym] of mixed products in two sets of variables. Recently, this class is been used in order to test some algebraic conjecture, including the conjecture of Eisenbud -Goto, on the symmetric algebra 〖Sym〗_S (L) .Since such conjecture involves fundamental invariants of Sym (L), such as the Krull dimension, the multiplicity and regularity of Castelnuovo-Mumford, it was necessary to calculate these invariants or their bounds. This problem is difficult, but if L is generated by a s-sequence, you can arrive at a concrete result. In the work Mixed…

A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families

2013

Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.

La linguistique cognitive existe-t-elle ?

2009

International audience; La présente contribution est consacrée à la question du statut théorique et de la légitimité même de la notion de ‘linguistique cognitive'. Sont tout d'abord rappelées (§ 1) les conditions historiques d'émergence, aux Etats-Unis, des deux grands courants de la linguistique dite ‘cognitive' : la grammaire générative (qui s'inscrit dans le paradigme ‘computo-représentationnel symbolique' du cognitivisme classique) et les grammaires cognitives (se réclamant d'un paradigme ‘constructiviste'). Puis (§ 2) est défendue l'idée qu'une théorie linguistique ne saurait se dire ‘cognitive' si elle ne cherche pas à relier explicitement les significations et les concepts, ce qui co…

Skyrmion formation due to unconventional magnetic modes in anisotropic multiband superconductors

2018

Multiband superconductors have a sufficient number of degrees of freedom to allow topological excitations characterized by Skyrmionic topological invariants. In the most common, clean s-wave multiband, systems the interband magnetic coupling favours composite vortex solutions, without a Skyrmionic topological charge. It was discussed recently that certain kinds of anisotropies lead to hybridisation of the interband phase difference (Leggett) mode with magnetic modes, dramatically changing the hydromagnetostatics of the system. Here we report this effect for a range of parameters that substantially alter the nature of the topological excitations, leading to solutions characterized by a nontr…

A cubic defining algebra for the Links-Gould polynomial

2012

We define a finite-dimensional cubic quotient of the group algebra of the braid group, endowed with a (essentially unique) Markov trace which affords the Links-Grould invariant of knots and links. We investigate several of its properties, and state several conjectures about its structure.

A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality

2019

AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s so…