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Homotopical Topology, Second Edition

Posted By: AvaxGenius
Date: 15 Oct 2023 14:20:40
Homotopical Topology, Second Edition

Homotopical Topology, Second Edition by Anatoly Fomenko , Dmitry Fuchs
English | PDF (True) | 2016 | 635 Pages | ISBN : 3319234870 | 27 MB

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).
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General Topology II: Compactness, Homologies of General Spaces

Posted By: AvaxGenius
Date: 19 Sep 2022 17:09:24
General Topology II: Compactness, Homologies of General Spaces

General Topology II: Compactness, Homologies of General Spaces by A. V. Arhangel’skii
English | PDF | 1996 | 265 Pages | ISBN : 3642770320 | 47.4 MB

This volume of the Encyclopaedia consists of two independent parts. The first contains a survey of results related to the concept of compactness in general topology. It highlights the role that compactness plays in many areas of general topology. The second part is devoted to homology and cohomology theories of general spaces. Special emphasis is placed on the method of sheaf theory as a unified approach to constructions of such theories. Both authors have succeeded in presenting a wealth of material that is of interest to students and researchers in the area of topology. Each part illustrates deep connections between important mathematical concepts. Both parts reflect a certain new way of looking at well known facts by establishing interesting relationships between specialized results belonging to diverse areas of mathematics.
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Sets, Logic and Categories

Posted By: AvaxGenius
Date: 10 Jul 2022 04:11:44
Sets, Logic and Categories

Sets, Logic and Categories by Peter J. Cameron
English | PDF | 1998 | 191 Pages | ISBN : 1852330562 | 14.8 MB

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.
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A1-Algebraic Topology over a Field (Repost)

Posted By: AvaxGenius
Date: 18 May 2022 21:52:06
A1-Algebraic Topology over a Field (Repost)

A1-Algebraic Topology over a Field by Fabien Morel
English | PDF | 2012 | 267 Pages | ISBN : 3642295134 | 2.5 MB

This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.
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Sheaves in Geometry and Logic: A First Introduction to Topos Theory

Posted By: AvaxGenius
Date: 1 Jul 2021 04:51:12
Sheaves in Geometry and Logic: A First Introduction to Topos Theory

Sheaves in Geometry and Logic: A First Introduction to Topos Theory by Saunders Mac Lane
English | PDF | 1994 | 642 Pages | ISBN : 0387977104 | 51.5 MB

We dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death.
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