Tag: Topology

September 9, 2024

A History of Algebraic and Differential Topology, 1900 – 1960

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Free Download A History of Algebraic and Differential Topology, 1900 – 1960 by Jean Dieudonné
English | PDF | 2009 | 666 Pages | ISBN : 0817649069 | 167.3 MB
Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

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April 25, 2024

Effective Non-Hermiticity and Topology in Markovian Quadratic Bosonic Dynamics

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Free Download Effective Non-Hermiticity and Topology in Markovian Quadratic Bosonic Dynamics
English | 2024 | ISBN: 3031520440 | 259 Pages | PDF EPUB (True) | 20 MB
This thesis provides an in-depth investigation of effective non-Hermiticity and topology in many-mode, non-interacting, bosonic systems. It also establishes the extent to which one must move beyond the Hamiltonian, closed-system setting, in order to uncover signatures of genuine symmetry-protected topological (SPT) physics in "free" (mean-field) bosons. While SPT phases of free fermionic matter and their associated zero-energy boundary-localized modes have been thoroughly explored, similar physics in free bosonic systems still remains elusive. No fermionic counterpart exists for the distinctive dynamical behavior that arises from the effective non-Hermiticity, intrinsic even at equilibrium, to bosonic Hamiltonians. Therefore, a much needed paradigm shift is required to address major conceptual roadblocks in the search for SPT bosonic phases.

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January 30, 2024

Topology II Homotopy and Homology. Classical Manifolds

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Free Download D.B. Fuchs, O.Ya. Viro, V.A. Rokhlin, "Topology II: Homotopy and Homology. Classical Manifolds"
English | 2004 | ISBN: 3642080847 | PDF | pages: 264 | 9.8 mb
Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

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January 21, 2024

Algebraic Topology A Structural Introduction

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Free Download Algebraic Topology: A Structural Introduction by Marco Grandis
English | December 29, 2021 | ISBN: 9811248354 | 372 pages | MOBI | 37 Mb
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout – the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation. This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites – basic general topology and little else – and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions. It can be used as a textbook for a semester course or self-study, and a guidebook for further study.

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January 16, 2024

The Pushing Points Topology Workbook

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Free Download The Pushing Points Topology Workbook by William C Vaughan
English | 2018 | ISBN: 1987728610 | 138 Pages | PDF | 91.5 MB
The Pushing Points Topology Workbook is a software agnostic guide that teaches you the foundation of SubD topology.

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January 15, 2024

Introduction to Piecewise-Linear Topology

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Free Download Introduction to Piecewise-Linear Topology by Colin P. Rourke , Brian J. Sanderson
English | PDF | 1982 | 133 Pages | ISBN : 3540111026 | 14.1 MB
The first five chapters of this book form an introductory course in piece wise-linear topology in which no assumptions are made other than basic topological notions. This course would be suitable as a second course in topology with a geometric flavour, to follow a first course in point-set topology, andi)erhaps to be given as a final year undergraduate course. The whole book gives an account of handle theory in a piecewise linear setting and could be the basis of a first year postgraduate lecture or reading course. Some results from algebraic topology are needed for handle theory and these are collected in an appendix. In a second appen dix are listed the properties of Whitehead torsion which are used in the s-cobordism theorem. These appendices should enable a reader with only basic knowledge to complete the book. The book is also intended to form an introduction to modern geo metric topology as a research subject, a bibliography of research papers being included. We have omitted acknowledgements and references from the main text and have collected these in a set of "historical notes" to be found after the appendices.

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