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Author | : Mark Grant |
Publisher | : American Mathematical Soc. |
Total Pages | : 176 |
Release | : 2018-02-14 |
Genre | : Algebraic topology |
ISBN | : 1470434369 |
Download Topological Complexity and Related Topics Book in PDF, ePub and Kindle
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28–March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach. Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik–Schnirelmann category and the Schwarz genus. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
Author | : Mark Grant |
Publisher | : |
Total Pages | : 176 |
Release | : 2018 |
Genre | : Algebraic topology |
ISBN | : 9781470444051 |
Download Topological Complexity and Related Topics Book in PDF, ePub and Kindle
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28 - March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach. Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik-Schnirelmann category and the Schwarz genus. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
Author | : |
Publisher | : |
Total Pages | : 38 |
Release | : 2015 |
Genre | : |
ISBN | : |
Download Mini-Workshop: Topological Complexity and Related Topics Book in PDF, ePub and Kindle
Author | : Robert Adler |
Publisher | : Springer Science & Business Media |
Total Pages | : 135 |
Release | : 2011-05-18 |
Genre | : Mathematics |
ISBN | : 3642195792 |
Download Topological Complexity of Smooth Random Functions Book in PDF, ePub and Kindle
These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
Author | : Michael Farber |
Publisher | : European Mathematical Society |
Total Pages | : 148 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190548 |
Download Invitation to Topological Robotics Book in PDF, ePub and Kindle
This book discusses several selected topics of a new emerging area of research on the interface between topology and engineering. The first main topic is topology of configuration spaces of mechanical linkages. These manifolds arise in various fields of mathematics and in other sciences, e.g., engineering, statistics, molecular biology. To compute Betti numbers of these configuration spaces the author applies a new technique of Morse theory in the presence of an involution. A significant result of topology of linkages presented in this book is a solution of a conjecture of Kevin Walker which states that the relative sizes of bars of a linkage are determined, up to certain equivalence, by the cohomology algebra of the linkage configuration space. This book also describes a new probabilistic approach to topology of linkages which treats the bar lengths as random variables and studies mathematical expectations of Betti numbers. The second main topic is topology of configuration spaces associated to polyhedra. The author gives an account of a beautiful work of S. R. Gal, suggesting an explicit formula for the generating function encoding Euler characteristics of these spaces. Next the author studies the knot theory of a robot arm, focusing on a recent important result of R. Connelly, E. Demain, and G. Rote. Finally, he investigates topological problems arising in the theory of robot motion planning algorithms and studies the homotopy invariant TC(X) measuring navigational complexity of configuration spaces. This book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering.
Author | : Naihuan Jing |
Publisher | : American Mathematical Soc. |
Total Pages | : 233 |
Release | : 2018-08-21 |
Genre | : Algebra |
ISBN | : 1470436965 |
Download Representations of Lie Algebras, Quantum Groups and Related Topics Book in PDF, ePub and Kindle
This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.
Author | : Steven M. LaValle |
Publisher | : Springer Nature |
Total Pages | : 573 |
Release | : 2022-12-14 |
Genre | : Technology & Engineering |
ISBN | : 3031210905 |
Download Algorithmic Foundations of Robotics XV Book in PDF, ePub and Kindle
This book includes significant recent research on robotic algorithms. It has been written by leading experts in the field. The 15th Workshop on the Algorithmic Foundations of Robotics (WAFR) was held on June 22–24, 2022, at the University of Maryland, College Park, Maryland. Each chapter represents an exciting state-of-the-art development in robotic algorithms that was presented at this 15th incarnation of WAFR. Different chapters combine ideas from a wide variety of fields, spanning and combining planning (for tasks, paths, motion, navigation, coverage, and patrol), computational geometry and topology, control theory, machine learning, formal methods, game theory, information theory, and theoretical computer science. Many of these papers explore new and interesting problems and problem variants that include human–robot interaction, planning and reasoning under uncertainty, dynamic environments, distributed decision making, multi-agent coordination, and heterogeneity.
Author | : Jonathan A. Barmak |
Publisher | : Springer Science & Business Media |
Total Pages | : 184 |
Release | : 2011-08-24 |
Genre | : Mathematics |
ISBN | : 3642220029 |
Download Algebraic Topology of Finite Topological Spaces and Applications Book in PDF, ePub and Kindle
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Author | : Michael Farber |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821842463 |
Download Topology and Robotics Book in PDF, ePub and Kindle
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
Author | : Petr Vojtěchovský |
Publisher | : American Mathematical Soc. |
Total Pages | : 297 |
Release | : 2019-01-14 |
Genre | : Nonassociative algebras |
ISBN | : 1470442450 |
Download Nonassociative Mathematics and its Applications Book in PDF, ePub and Kindle
Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.