Algebraic Topology

Part 2 book "A course in modern mathematical physics - Froups, hilbert space and differential geometry" includes content: Topology, measure theory andintegration, distributions, hilbert spaces, quantum mechanics, differential geometry, differentiable forms, integration on manifolds, connections and curvature, lie groups and lie algebras.

346p muasambanhan10 06-04-2024 3 0   Download

Continued part 1, part 2 of lecture Topology presents the following content: algebraic topology; structures on topological spaces; classification of compact surfaces; homotopy; the fundamental group; the fundamental group of the circle; differential topology; tangent spaces and derivatives;...

139p damtuyetha 09-01-2023 8 2   Download

Ebook All the mathematics you missed: but need to know for graduate school - Part 1 presents the following chapters: Chapter 1 linear algebra, chapter 2 ϵ and δ real analysis, chapter 3 calculus for vector-valued functions, chapter 4 point set topology, chapter 5 classical Stokes' Theorems, chapter 6 differential forms and Stokes' theorem.

173p runthenight04 04-01-2023 20 5   Download

In this paper, we describe in detail some main occurrences of crossed modules. These are the common classes of crossed modules in algebra and topology. For every class of crossed modules, we also look for the analogues and show their special property.

7p trinhthamhodang1218 18-03-2021 5 2   Download

Understanding protein structure and dynamics is essential for understanding their function. This is a challenging task due to the high complexity of the conformational landscapes of proteins and their rugged energy levels. In particular, it is important to detect highly populated regions which could correspond to intermediate structures or local minima.

9p viconnecticut2711 29-10-2020 13 1   Download

The paper is a continuation of the authors’ works [18], [19]. In [18], we consider foliations formed by the maximal dimensional K-orbits (MD5-foliations) of connected MD5-groups that their Lie algebras have 4-dimensional commutative derived ideals and give a topological classification of the considered foliations. In [19], we study K-theory of the leaf space of some of these MD5-foliations, analytically describe and characterize the Connes’ C*-algebras of the considered foliations by the method of K-functors.

10p gaunguyen6789 19-10-2019 27 0   Download

Let Cb(X) be the C∗-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space X. Moreover, let A0 be some ideal and A1 be some unital C-subalgebra of Cb(X). For A0 and A1 having trivial intersection, we show that the spectrum of their vector space sum equals the disjoint union of their individual spectra, whereas their topologies are nontrivially interwoven.

14p viryucha2711 24-04-2019 24 0   Download

Locally symmetric spaces play an important part in differential geometry and arise from many different areas such as topology, number theory, representation theory, algebraic geometry,...The typical important class consists of quotients of symmetric spaces by arithmetic groups, for example, the moduli space of elliptic curves is the quotient of the upper half plane H2 by SL(2, Z).

9p thiendiadaodien_9 04-03-2019 31 0   Download

We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.

12p nutifooddau 21-01-2019 22 1   Download

In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent.

13p danhdanh27 07-01-2019 14 1   Download

In this paper, we will prove some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operators acting on a WC–Banach algebra. Our results improve and correct some recent results given by Banas and Taoudi, and extend several earlier works using the condition (P).

9p danhdanh27 07-01-2019 24 1   Download

Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set X(A), of all continuous multiplicative linear functionals, is not empty.

21p danhdanh27 07-01-2019 17 2   Download

In this paper we study the dual space of fundamental locally multiplicative topological algebras and prove some results for linear and multiplicative linear functionals on these algebras. An investigation on locally compactness of the carrier space of these algebras is the last part of this note.

7p tuongvidanh 06-01-2019 18 1   Download

In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by F LM ). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.

7p tuongvidanh 06-01-2019 30 1   Download

In order to improve quality-of-service of distributed applications, we propose a multi-criteria algorithm based on interpolative Boolean algebra for routing in an overlay network. We use a mesh topology because its implementation is easy and it quite simple addresses the cores during routing. In this paper, we consider four criteria: buffer usage, distance between peers, bandwidth, and remaining battery power.

16p vinguyentuongdanh 19-12-2018 20 0   Download

(BQ) Part 2 book "A first course in abstract algebra" has contents: Extention fields, advanced group theory, groups in topology, factorization, automorphisms and galois theory.

251p bautroibinhyen19 02-03-2017 44 6   Download

Such jobs would then be gone, to be replaced by jobs requiring much more sophisticated mathematical training. The mathematics needed for these machines, as was case with engines, has been the main impediment to actual wide-scale implementation of such robotic mechanisms. Recently, it has become clear that the key mathematics is available, (the mathematics of algebraic and geometric topology, developed over the last 80 - 90 years), and we have begun to make dramatic progress in creating the programs needed to make such machines work.

276p dacotaikhoan 25-04-2013 106 9   Download

The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

28p noel_noel 17-01-2013 49 6   Download

Let k be a local field, and Γ ≤ GLn (k) a linear group over k. We prove that Γ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. Contents 1. Introduction 2. A generalization of a lemma of Tits 3. Contracting projective transformations 4. Irreducible representations of non-Zariski connected algebraic groups 5. Proof of Theorem 1.3 in the finitely generated case 6. Dense free subgroups with infinitely many generators 7.

49p noel_noel 17-01-2013 53 6   Download

We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is deduced from the main result about finite groups: let w be a ‘locally finite’ group word and d ∈ N. Then there exists f = f (w, d) such that in every d-generator finite group G, every element of the verbal subgroup w(G) is equal to a product of f w-values.

69p noel_noel 17-01-2013 47 7   Download