Combinatorial And Toric Homotopy: Introductory Lectures

2017-10-20 Mathematics

Author : Alastair Darby
Release : 2017-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Combinatorial And Toric Homotopy: Introductory Lectures by : Alastair Darby

Download or read book Combinatorial And Toric Homotopy: Introductory Lectures written by Alastair Darby. This book was released on 2017-10-20. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.

Combinatorial and Toric Homotopy

2018 Combinatorial topology

Author : Alastair Darby
Release : 2018
Genre : Combinatorial topology
Kind : eBook
Book Rating : 579/5 ( reviews)

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Book Synopsis Combinatorial and Toric Homotopy by : Alastair Darby

Download or read book Combinatorial and Toric Homotopy written by Alastair Darby. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: "This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students."--Publisher's website.

Toric Topology

2015-07-15 Mathematics

Author : Victor M. Buchstaber
Release : 2015-07-15
Genre : Mathematics
Kind : eBook
Book Rating : 14X/5 ( reviews)

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Book Synopsis Toric Topology by : Victor M. Buchstaber

Download or read book Toric Topology written by Victor M. Buchstaber. This book was released on 2015-07-15. Available in PDF, EPUB and Kindle. Book excerpt: This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.

Toric Topology

2008 Mathematics

Author : Megumi Harada
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 865/5 ( reviews)

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Book Synopsis Toric Topology by : Megumi Harada

Download or read book Toric Topology written by Megumi Harada. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the fieldare provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry.This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above. Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students andresearchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.

Combinatorial Homotopy and 4-dimensional Complexes

1991 Mathematics

Author : Hans J. Baues
Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : 880/5 ( reviews)

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Book Synopsis Combinatorial Homotopy and 4-dimensional Complexes by : Hans J. Baues

Download or read book Combinatorial Homotopy and 4-dimensional Complexes written by Hans J. Baues. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt: The bulk of the book is devoted to the algebraic theory of quadratic modules and their connections with 4-dimensional complexes, Pontrjagin squares, homotopy groups, the cohomology of categories, and algebraic K-theory. The first three chapters provide the background needed and may serve as an introduction to basic combinatorial homotopy theory. Annotation copyrighted by Book News, Inc., Portland, OR

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