Lecture Notes in Mathematics

Operads of Wiring Diagrams

Authors: Yau, Donald

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  • Provides a self-contained introduction to wiring diagrams, operads, and operad algebras
  • Includes over 100 illustrations and a chapter of practice problems
  • Presents generators and relations for both the operads and algebras of wiring diagrams introduced by David Spivak
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eBook $44.99
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  • ISBN 978-3-319-95001-3
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Softcover $59.99
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  • ISBN 978-3-319-95000-6
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  • Usually dispatched within 3 to 5 business days.
About this book

Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads.

The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak’s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images.

Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.

About the authors

Donald Yau is Professor of Mathematics at The Ohio State University at Newark. He obtained his PhD at MIT and held a post-doctoral position at the University of Illinois at Urbana-Champaign. His research focuses on algebraic topology. He has so far authored five books and over 30 articles.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-95001-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-95000-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Operads of Wiring Diagrams
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2192
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-95001-3
DOI
10.1007/978-3-319-95001-3
Softcover ISBN
978-3-319-95000-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XI, 308
Number of Illustrations
437 b/w illustrations
Topics