Basic Topology 3: Algebraic Topology and Topology of Fiber Bundles

Adhikari, Mahima Ranjan

Basic Topology 3: Algebraic Topology and Topology of Fiber Bundles
  • 出版商: Springer
  • 出版日期: 2024-03-17
  • 售價: $2,480
  • 貴賓價: 9.5 折 $2,356
  • 語言: 英文
  • 頁數: 468
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 9811665524
  • ISBN-13: 9789811665523

    • 海外代購書籍(需單獨結帳)

商品描述

This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.

商品描述(中文翻譯)

這本三卷本書籍的第三卷旨在為數學的本科生和研究生提供一個基礎課程，內容涵蓋代數拓撲和纖維束的拓撲。它專注於拓撲的多種變體及其在現代分析、幾何和代數中的應用。本卷涵蓋的主題包括同倫理論、同調與上同調理論、纖維束的同倫理論、歐拉特徵數以及Betti數。它還包括一些經典問題，例如喬丹曲線定理，並討論了更高的同倫群，建立了同倫與同調理論之間的聯繫，以及Eilenberg和Steenrod所開創的同調與上同調的公理化方法。本書的內容超出了初學者在一學期課程中能夠輕鬆掌握的範圍。進階課程的學生也會發現本書非常有用。本書將促進該學科的範疇、力量和主動學習，同時以平衡統一的方式涵蓋廣泛的理論和應用。

作者簡介

MAHIMA RANJAN ADHIKARI, Ph.D., M.Sc. (Gold Medalist), is the founder president of the Institute for Mathematics, Bioinformatics and Computer Science (IMBIC), Kolkata, India. He is a former professor at the Department of Pure Mathematics, University of Calcutta, India. His research papers are published in national and international journals of repute, including the Proceedings of American Mathematical Society. He has authored nine textbooks and is the editor of two, including: Basic Modern Algebra with Applications (Springer, 2014), Basic Algebraic Topology and Applications (Springer, 2016), and Mathematical and Statistical Applications in Life Sciences and Engineering (Springer, 2017).

Twelve students have been awarded Ph.D. degree under his guidance on various topics such as algebra, algebraic topology, category theory, geometry, analysis, graph theory, knot theory and history of mathematics. He has visited several universities and research institutions in India, USA, UK, Japan, China, Greece, Sweden, Switzerland, Italy, and many other counties on invitation. A member of the American Mathematical Society, Prof. Adhikari is on the editorial board of several journals of repute. He was elected as the president of the Mathematical Sciences Section (including Statistics) of the 95th Indian Science Congress, 2008. He has successfully completed research projects funded by the Government of India.

作者簡介(中文翻譯)

MAHIMA RANJAN ADHIKARI 博士，碩士（金牌得主），是印度加爾各答數學、生物資訊與計算機科學研究所（IMBIC）的創始會長。他曾任印度加爾各答大學純數學系教授。他的研究論文發表於多個國內外知名期刊，包括《美國數學學會會議錄》。他著有九本教科書，並編輯兩本，包括《基本現代代數及其應用》（Springer, 2014）、《基本代數拓撲及其應用》（Springer, 2016）和《生命科學與工程中的數學與統計應用》（Springer, 2017）。

在他的指導下，有十二名學生在代數、代數拓撲、範疇論、幾何、分析、圖論、結理論及數學史等各種主題上獲得博士學位。他曾應邀訪問印度、美國、英國、日本、中國、希臘、瑞典、瑞士、義大利及其他多個國家的多所大學和研究機構。作為美國數學學會的成員，Adhikari 教授擔任多個知名期刊的編輯委員會成員。他於2008年第95屆印度科學大會上當選數學科學分會（包括統計學）會長。他成功完成了由印度政府資助的研究項目。

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