The algebraic topology

Lecture notes on topology and geometry present on: General Topology, Algebraic Topology, Differential Topology, Differential Geometry, Differentiable manifolds,... Invite you to refer to the lecture content more learning materials and research.
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Surveying a vast theory like Teichmüller theory is like surveying a land, and the various chapters in this Handbook are like a collection of maps forming an atlas: some of them give a very general overview of the field, others give a detailed view of some crowded area, and others are more focussed on interesting details. There are intersections between the chapters, and these intersections are necessary.
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Surveying a vast theory like Teichmüller theory is like surveying a land, and the various chapters in this Handbook are like a collection of maps forming an atlas: some of them give a very general overview of the field, others give a detailed view of some crowded area, and others are more focussed on interesting details. There are intersections between the chapters, and these intersections are necessary.
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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 17012013 21 5 Download

Israel Moiseevich Gelfand is one of the greatest mathematicians of the 20th century. His insights and ideas have helped to develop new areas in mathematics and to reshape many classical ones. The influence of Gelfand can be found everywhere in mathematics and mathematical physics from functional analysis to geometry, algebra, and number theory. His seminar (one of the most influential in the history of mathematics) helped to create a very diverse and productive Gelfand school; indeed, many outstanding mathematicians proudly call themselves Gelfand disciples....
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Ten years ago Elsevier published the volume Recent Progress in General Topology. The idea behind that book was to present surveys describing recent developments in most of the primary subfields of General Topology and its applications to Algebra and Analysis. It was our belief that the book could be of help to researchers in General Topology as a background for the development of their own research. There were two similar predecessors, namely, the Handbook of SetTheoretic Topology (North Holland, Amsterdam 1984, J.E. Vaughan and K. Kunen, eds.
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SAMUEL EILENBERG. Automata, Languages, and Machines: Volumes A and B MORRIS HIRSCH N D STEPHEN A SMALE. Differential Equations, Dynamical Systems, and Linear Algebra WILHELM MAGNUS. Noneuclidean Tesselations and Their Groups FRANCOIS TREVES. Linear Partial Differential Equations Basic WILLIAM BOOTHBY. Introduction to Differentiable Manifolds and Riemannian M. An Geometry ~ A Y T O N GRAY. Homotopy Theory : An Introduction to Algebraic Topology ROBERT ADAMS. A. Sobolev Spaces JOHN BENEDETTO. J. Spectral Synthesis D. V. WIDDER.
291p mrbin1262006 06052010 91 23 Download

We show that unital simple C ∗ algebras with tracial topological rank zero which are locally approximated by subhomogeneous C ∗ algebras can be classiﬁed by their ordered Ktheory. We apply this classiﬁcation result to show that certain simple crossed products are isomorphic if they have the same ordered Ktheory. In particular, irrational higher dimensional noncommutative tori of the form C(Tk ) ×θ Z are in fact inductive limits of circle algebras. Introduction In recent years there has been rapid progress in classiﬁcation of nuclear simple C ...
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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 widescale 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.
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Topological Hochschild homology and localization 2. The homotopy groups of T (AK) 3. The de RhamWitt complex and TR· (AK; p) ∗ 4. Tate cohomology and the Tate spectrum 5. The Tate spectral sequence for T (AK) 6. The prosystem TR· (AK; p, Z/pv ) ∗ Appendix A. Truncated polynomial algebras References Introduction In this paper we establish a connection between the Quillen Ktheory of certain local ﬁelds and the de RhamWitt complex of their rings of integers with logarithmic poles at the maximal ideal.
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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 dgenerator ﬁnite group G, every element of the verbal subgroup w(G) is equal to a product of f wvalues.
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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 nonZariski connected algebraic groups 5. Proof of Theorem 1.3 in the ﬁnitely generated case 6. Dense free subgroups with inﬁnitely many generators 7.
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The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz [L] and Zariski [Z] and is always present on the scene; see for instance the work by Libgober [Li]. In this paper we study complements of hypersurfaces, with special attention to the case of hyperplane arrangements as discussed in OrlikTerao’s book [OT1]. Theorem 1 expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of ncells that have to be added to a generic hyperplane section D(h) ∩ H to obtain the complement in...
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Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Ngày thứ hạng ổn định topo đại số luân chuyển không hợp lý...
8p matuot_266 27082011 16 2 Download

This book is an elaboration of ideas of Irving Kaplansky introduced in his book Rings of operators ([52], [54]). The subject of Baer *rings has its roots in von Neumann's theory of 'rings of operators' (now called von Neumann algebras), that is, *algebras of operators on a Hilbert space, containing the identity operator, that are closed in the weak operator topology (hence also the name W*algebra).
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