اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدQuillen Suslin theory for algebraic fundamental group
121
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we attempt to develop the Quillen Suslin theory for the algebraic fundamental group of a ring. We give a surjective group homomorphism from the algebraic fundamental group of the field of the real numbers to the group of integers. At the end of the paper, we also propose some problems related to the algebraic fundamental group of some particular type of rings.
قيم البحث
اقرأ أيضاً
We study algebraic and topological properties of subsets of preorders on a group. In particular we study properties of the composition of two preorders, generalize a topological theorem of cite{S} in the case of standard orders and show the same theo
rem in the case of standard preorders. We also show a property of standard valuations.
We resolve a conjecture of Kalai asserting that the $g_2$-number of any simplicial complex $Delta$ that represents a connected normal pseudomanifold of dimension $dgeq 3$ is at least as large as ${d+2 choose 2}m(Delta)$, where $m(Delta)$ denotes the
minimum number of generators of the fundamental group of $Delta$. Furthermore, we prove that a weaker bound, $h_2(Delta)geq {d+1 choose 2}m(Delta)$, applies to any $d$-dimensional pure simplicial poset $Delta$ all of whose faces of co-dimension $geq 2$ have connected links. This generalizes a result of Klee. Finally, for a pure relative simplicial poset $Psi$ all of whose vertex links satisfy Serres condition $(S_r)$, we establish lower bounds on $h_1(Psi),ldots,h_r(Psi)$ in terms of the $mu$-numbers introduced by Bagchi and Datta.
This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on combinatorics, t
opology, and geometry of a simplicial or polyhedral subdivision of a region in R^k, and are often quite subtle. We describe four algebraic techniques which are useful in the study of splines: homology, graded algebra, localization, and inverse systems. Our goal is to give a hands-on introduction to the methods, and illustrate them with concrete examples in the context of splines. We highlight progress made with these methods, such as a formula for the third coefficient of the polynomial giving the dimension of the spline space in high degree, much of which builds on pioneering work of Schumaker, Alfeld-Schumaker, and Billera. The objects appearing here may be computed using the Macaulay2 software system.
Let $n$ be a positive integer and let $f_1, ldots, f_r$ be polynomials in $n^2$ indeterminates over an algebraically closed field $K$. We describe an algorithm to decide if the invertible matrices contained in the variety of $f_1, ldots, f_r$ form a
subgroup of $GL(n,K)$; that is, we show how to decide if the polynomials $f_1, ldots, f_r$ define a linear algebraic group.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
