اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRen{e} Thom and an anticipated h-principle
49
0
0.0
(
0
)
تأليف
Francois Laudenbach
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The first part of this article intends to present the role played by Thom in diffusing Smales ideas about immersion theory, at a time (1957) where some famous mathematicians were doubtful about them: it is clearly impossible to make the sphere inside out! Around a decade later, M. Gromov transformed Smales idea in what is now known as the h-principle. Here, the h stands for homotopy.Shortly after the astonishing discovery by Smale, Thom gave a conference in Lille (1959) announcing a theorem which would deserve to be named a homological h-principle. The aim of our second part is to comment about this theorem which was completely ignored by the topologists in Paris, but not in Leningrad. We explain Thoms statement and answer the question whether it is true. The first idea is combinatorial. A beautiful subdivision of the standard simplex emerges from Thoms article. We connect it with the jiggling technique introduced by W. Thurston in his seminal work on foliations.
قيم البحث
اقرأ أيضاً
Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are encircled and no
two lines can overlap over a finite length. The mathematical foundation for this art form has attracted attention over the years. In this work, we propose a simple 5-step topological method by which one can systematically draw all possible kolams for any number of dots N arranged in any spatial configuration on a surface.
The aim of this short note is to provide three geometric visualizations of a fascinating inequality $b^{e}<e^{b}$ when $e<b$.
We search for rare decays of $D$ mesons to hadrons accompany with an electron-positron pair (h(h)$e^+e^-$), using an $e^+e^-$ collision sample corresponding to an integrated luminosity of 2.93 fb$^{-1}$ collected with the BESIII detector at $sqrt{s}$
= 3.773 GeV. No significant signals are observed, and the corresponding upper limits on the branching fractions at the $90%$ confidence level are determined. The sensitivities of the results are at the level of $10^{-5} sim 10^{-6}$, providing a large improvement over previous searches.
We present some episodes from the history of interactions between geometry and physics over the past century.
We estimate the upper bound for the $ell^{infty}$-norm of the volume form on $mathbb{H}^2timesmathbb{H}^2timesmathbb{H}^2$ seen as a class in $H_{c}^{6}(mathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R}timesmathrm{PSL}_{2}mathbb{R};mathbb{R})$. T
his gives the lower bound for the simplicial volume of closed Riemennian manifolds covered by $mathbb{H}^{2}timesmathbb{H}^{2}timesmathbb{H}^{2}$. The proof of these facts yields an algorithm to compute the lower bound of closed Riemannian manifolds covered by $big(mathbb{H}^2big)^n$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
