Topology and Condensed Matter Physics

This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics

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Somendra Mohan Bhattacharjee Mahan Mj Abhijit Bandyopadhyay Editors

Topology and Condensed Matter Physics

Texts and Readings in Physical Sciences Volume 19

Managing Editors H. S. Mani, Chennai Mathematical Institute, Chennai Ram Ramaswamy, Jawaharlal Nehru University, New Delhi Editors Kedar Damle, Tata Institute of Fundamental Research, Mumbai Debashis Ghoshal, Jawaharlal Nehru University, New Delhi Rajaram Nityananda, National Centre for Radio Astrophysics, Pune Gautam Menon, Institute of Mathematical Sciences, Chennai Tarun Souradeep, Inter-University Centre for Astronomy and Astrophysics, Pune

The Texts and Readings in Physical Sciences series publishes high-quality textbooks, research-level monographs, lecture notes and contributed volumes. Undergraduate and graduate students of physical sciences and applied mathematics, research scholars and teachers would find this book series useful. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. The books in this series are co-published with Hindustan Book Agency, New Delhi, India.

More information about this series at http://www.springer.com/series/15139

Somendra Mohan Bhattacharjee Mahan Mj Abhijit Bandyopadhyay •

Editors

Topology and Condensed Matter Physics

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Editors Somendra Mohan Bhattacharjee Institute of Physics Bhubaneswar, Odisha India Mahan Mj School of Mathematics Tata Institute of Fundamental Research Mumbai, Maharashtra India

Abhijit Bandyopadhyay Department of Physics Ramakrishna Mission Vivekananda University Howrah, West Bengal India

This work is a co-publication with Hindustan Book Agency, New Delhi, licensed for sale in all countries in electronic form, in print form only outside of India. Sold and distributed in print within India by Hindustan Book Agency, P-19 Green Park Extension, New Delhi 110016, India. ISBN: 978-93-86279-66-8 © Hindustan Book Agency 2017. ISSN 2366-8849 ISSN 2366-8857 (electronic) Texts and Readings in Physical Sciences ISBN 978-981-10-6840-9 ISBN 978-981-10-6841-6 (eBook) https://doi.org/10.1007/978-981-10-6841-6 Library of Congress Control Number: 2017955364 © Springer Nature Singapore Pte Ltd. 2017 and Hindustan Book Agency 2017 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in th

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