Homology And Cohomology A Primer For Undergraduates Through Applications
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Homology And Cohomology A Primer For Undergraduates Through Applications
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Author : Luca Vitagliano
language : en
Publisher: World Scientific
Release Date : 2025-04-14
Homology And Cohomology A Primer For Undergraduates Through Applications written by Luca Vitagliano and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-14 with Mathematics categories.
The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergraduate Mathematics students, as well as graduate and postgraduate students in other fields, particularly Theoretical Physics, who require a highly compact overview of this vast theory. The book also explores how (co)homology theory naturally arises in seemingly unrelated areas of Mathematics.The theory is presented from scratch, requiring no prerequisites other than basic linear algebra, point-set topology, and calculus. The presentation is simple, concise, yet rigorous, making it accessible to undergraduate Mathematics and likely Physics students from the third year onward. The book emphasizes the theory's numerous applications across Algebra and Geometry, rather than focusing solely on the theoretical aspects. The pedagogical approach of this book, complemented by examples and exercises, sets it apart from standard textbooks in Homological Algebra and Algebraic Topology. The end-of-chapter problems offer insight into more advanced material and serve as a tool for testing comprehension of the theory.After having gone through these lecture notes, the reader will be ready to tackle more specialized and advanced subjects such as Homological Algebra, Homotopy Theory, and Algebraic Topology.
Homology Cohomology
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Author : Luca Vitagliano
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025
Homology Cohomology written by Luca Vitagliano and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Mathematics categories.
The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergraduate Mathematics students, as well as graduate and postgraduate students in other fields, particularly Theoretical Physics, who require a highly compact overview of this vast theory. The book also explores how (co)homology theory naturally arises in seemingly unrelated areas of Mathematics.The theory is presented from scratch, requiring no prerequisites other than basic linear algebra, point-set topology, and calculus. The presentation is simple, concise, yet rigorous, making it accessible to undergraduate Mathematics and likely Physics students from the third year onward. The book emphasizes the theory's numerous applications across Algebra and Geometry, rather than focusing solely on the theoretical aspects. The pedagogical approach of this book, complemented by examples and exercises, sets it apart from standard textbooks in Homological Algebra and Algebraic Topology. The end-of-chapter problems offer insight into more advanced material and serve as a tool for testing comprehension of the theory.After having gone through these lecture notes, the reader will be ready to tackle more specialized and advanced subjects such as Homological Algebra, Homotopy Theory, and Algebraic Topology.
A Primer Of Algebraic Geometry
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Author : Huishi Li
language : en
Publisher: CRC Press
Release Date : 2017-12-19
A Primer Of Algebraic Geometry written by Huishi Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."
Algebraic Topology
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Author : Satya Deo
language : en
Publisher: Springer
Release Date : 2003-12-01
Algebraic Topology written by Satya Deo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-01 with Mathematics categories.
Group Actions And Equivariant Cohomology
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Author : Loring W. Tu
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-26
Group Actions And Equivariant Cohomology written by Loring W. Tu and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-26 with Mathematics categories.
This volume contains the proceedings of the virtual AMS Special Session on Equivariant Cohomology, held March 19?20, 2022. Equivariant topology is the algebraic topology of spaces with symmetries. At the meeting, ?equivariant cohomology? was broadly interpreted to include related topics in equivariant topology and geometry such as Bredon cohomology, equivariant cobordism, GKM (Goresky, Kottwitz, and MacPherson) theory, equivariant $K$-theory, symplectic geometry, and equivariant Schubert calculus. This volume offers a view of the exciting progress made in these fields in the last twenty years. Several of the articles are surveys suitable for a general audience of topologists and geometers. To be broadly accessible, all the authors were instructed to make their presentations somewhat expository. This collection should be of interest and useful to graduate students and researchers alike.
Perturbed Gradient Flow Trees And A Algebra Structures In Morse Cohomology
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Author : Stephan Mescher
language : en
Publisher: Springer
Release Date : 2018-04-25
Perturbed Gradient Flow Trees And A Algebra Structures In Morse Cohomology written by Stephan Mescher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-25 with Mathematics categories.
This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse functions. To make A∞-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid’s approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained. In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
Algebraic Topology Applications And New Directions
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Author : Ulrike Tillmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-07-14
Algebraic Topology Applications And New Directions written by Ulrike Tillmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.
Equivariant Cohomology Of Configuration Spaces Mod 2
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Author : Pavle V. M. Blagojević
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Equivariant Cohomology Of Configuration Spaces Mod 2 written by Pavle V. M. Blagojević and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(R^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and l-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.
More Concise Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 2011-12-05
More Concise Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-05 with Mathematics categories.
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.
Aspects Of Infinite Groups A Festschrift In Honor Of Anthony Gaglione
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Author : Benjamin Fine
language : en
Publisher: World Scientific
Release Date : 2008-10-23
Aspects Of Infinite Groups A Festschrift In Honor Of Anthony Gaglione written by Benjamin Fine and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-23 with Mathematics categories.
This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.