Topological Homology PDF Download
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Author | : Tamal Krishna Dey |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 2022-03-10 |
Genre | : Mathematics |
ISBN | : 1009103199 |
Download Computational Topology for Data Analysis Book in PDF, ePub and Kindle
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Author | : Ralph L. Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 159 |
Release | : 2006-03-21 |
Genre | : Mathematics |
ISBN | : 3764373881 |
Download String Topology and Cyclic Homology Book in PDF, ePub and Kindle
This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.
Author | : Hiro Lee Tanaka |
Publisher | : Springer Nature |
Total Pages | : 84 |
Release | : 2020-12-14 |
Genre | : Science |
ISBN | : 3030611639 |
Download Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories Book in PDF, ePub and Kindle
This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
Author | : Bjørn Ian Dundas |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2012-09-06 |
Genre | : Mathematics |
ISBN | : 1447143930 |
Download The Local Structure of Algebraic K-Theory Book in PDF, ePub and Kindle
Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Author | : Steve Y. Oudot |
Publisher | : American Mathematical Soc. |
Total Pages | : 229 |
Release | : 2017-05-17 |
Genre | : Mathematics |
ISBN | : 1470434431 |
Download Persistence Theory: From Quiver Representations to Data Analysis Book in PDF, ePub and Kindle
Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Author | : Andrew H. Wallace |
Publisher | : Courier Corporation |
Total Pages | : 290 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486462390 |
Download Algebraic Topology Book in PDF, ePub and Kindle
Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.
Author | : James W. Vick |
Publisher | : Springer Science & Business Media |
Total Pages | : 258 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208815 |
Download Homology Theory Book in PDF, ePub and Kindle
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Author | : |
Publisher | : Nova Biomedical Books |
Total Pages | : 230 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : |
Download Topological Homology Book in PDF, ePub and Kindle
Contains some results obtained during seminars over the last few years. The seven papers discuss stereotype spaces, algebras and homologies; flat operator modules and their dual modules; homological dimensions of C*- algebras; Wedderburn-type theorems for operator algebras and modules; injective topological modules and additivity formulas for homological dimensions; coretraction problems and homological properties of Banach algebras; and the Sobolev algebra and indecomposable spatially projective operator algebras.
Author | : William S. Massey |
Publisher | : Springer |
Total Pages | : 448 |
Release | : 2019-06-28 |
Genre | : Mathematics |
ISBN | : 1493990632 |
Download A Basic Course in Algebraic Topology Book in PDF, ePub and Kindle
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
Author | : Tomasz Kaczynski |
Publisher | : Springer Science & Business Media |
Total Pages | : 488 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387215972 |
Download Computational Homology Book in PDF, ePub and Kindle
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.