اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA proof of Morses theorem about the cancellation of critical points
107
0
0.0
(
0
)
تأليف
Francois Laudenbach
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer.
قيم البحث
اقرأ أيضاً
Heegaard splittings and Heegaard diagrams of a closed 3-manifold M are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on M. We make use in a very simple setting of techniques which Jean Cerf developed for so
lving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when dim M>2. The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
We give a general method of extending unital completely positive maps to amalgamated free products of C*-algebras. As an application we give a dilation theoretic proof of Bocas Theorem.
The Hilbert-Smith Conjecture states that if G is a locally compact group which acts effectively on a connected manifold as a topological transformation group, then G is a Lie group. A rather straightforward proof of this conjecture is given. The moti
vation is work of Cernavskii (``Finite-to-one mappings of manifolds, Trans. of Math. Sk. 65 (107), 1964.) His work is generalized to the orbit map of an effective action of a p-adic group on compact connected n-manifolds with the aid of some new ideas. There is no attempt to use Smith Theory even though there may be similarities.
The Modified Szpiro Conjecture, equivalent to the $abc$ Conjecture, states that for each $epsilon>0$, there are finitely many rational elliptic curves satisfying $N_{E}^{6+epsilon}<max!left{ leftvert c_{4}^{3}rightvert,c_{6}^{2}right} $ where $c_{4}$
and $c_{6}$ are the invariants associated to a minimal model of $E$ and $N_{E}$ is the conductor of $E$. We say $E$ is a good elliptic curve if $N_{E}^{6}<max!left{ leftvert c_{4}^{3}rightvert,c_{6}^{2}right} $. Masser showed that there are infinitely many good Frey curves. Here we give a constructive proof of this assertion.
Greenberg proved that every countable group $A$ is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if $A$ is finite. We give a short and explicit algebraic proof of this for finitely generated groups $A$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
