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What is the Genus?
Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Al…
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- ISBN/ISSN
- 978-3-319-42312-8
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The Scottish Book
The second edition of this book updates and expands upon a historically important collection of mathematical problems first published in the United States by Birkhäuser in 1981. These problems serve as a record of the informal discussions held by a group of mathematicians at the Scottish Café in Lwów, Poland, between the two world wars. Many of them were leaders in the development of such ar…
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- 1
- ISBN/ISSN
- 978-3-319-22897-6
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Simplicial and Dendroidal Homotopy Theory
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplic…
- Edition
- 1
- ISBN/ISSN
- 978-3-031-10447-3
- Collation
- Mathematics
- Series Title
- Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
- Call Number
- 510
A Geometric Approach to Homology Theory
The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology …
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- ISBN/ISSN
- 9780511662669
- Collation
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- Series Title
- London Mathematical Society Lecture Note Series (18)
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A Gentle Introduction to Homological Mirror Symmetry
Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great de…
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- ISBN/ISSN
- 9781108692458
- Collation
- -
- Series Title
- London Mathematical Society Student Texts (99)
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Equivariant Ordinary Homology and Cohomology
Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through so…
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- ISBN/ISSN
- 978-3-319-50448-3
- Collation
- 1 b/w illustrations
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- -
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A First Course in Computational Algebraic Geometry
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using th…
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- ISBN/ISSN
- 9781139565769
- Collation
- -
- Series Title
- AIMS Library of Mathematical Sciences
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A First Course in Algebraic Topology
This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the Univer…
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- ISBN/ISSN
- 9780511569296
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- -
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Topology and Geometric Group Theory Ohio State University, Columbus, USA, 20…
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over t…
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- ISBN/ISSN
- 978-3-319-43674-6
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- -
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Topology
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov comp…
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- ISBN/ISSN
- 978-3-319-16958-3
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