A Guide to the Classification Theorem for Compact Surfaces

Author: Jean Gallier,Dianna Xu

Publisher: Springer Science & Business Media

ISBN: 3642343643

Category: Mathematics

Page: 178

View: 6237


This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

Handbook of Geometric Computing

Applications in Pattern Recognition, Computer Vision, Neuralcomputing, and Robotics

Author: Eduardo Bayro Corrochano

Publisher: Springer Science & Business Media

ISBN: 3540282475

Category: Computers

Page: 779

View: 6909


Many computer scientists, engineers, applied mathematicians, and physicists use geometry theory and geometric computing methods in the design of perception-action systems, intelligent autonomous systems, and man-machine interfaces. This handbook brings together the most recent advances in the application of geometric computing for building such systems, with contributions from leading experts in the important fields of neuroscience, neural networks, image processing, pattern recognition, computer vision, uncertainty in geometric computations, conformal computational geometry, computer graphics and visualization, medical imagery, geometry and robotics, and reaching and motion planning. For the first time, the various methods are presented in a comprehensive, unified manner. This handbook is highly recommended for postgraduate students and researchers working on applications such as automated learning; geometric and fuzzy reasoning; human-like artificial vision; tele-operation; space maneuvering; haptics; rescue robots; man-machine interfaces; tele-immersion; computer- and robotics-aided neurosurgery or orthopedics; the assembly and design of humanoids; and systems for metalevel reasoning.

Elements of Differential Topology

Author: Anant R. Shastri

Publisher: CRC Press

ISBN: 1439831637

Category: Mathematics

Page: 319

View: 6877


Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topol

Problems on Mapping Class Groups and Related Topics

Author: Benson Farb

Publisher: American Mathematical Soc.

ISBN: 0821838385

Category: Mathematics

Page: 371

View: 3557


This book contains 23 papers of open problems and directions about mapping class groups and related topics. The papers focus on aspects deeply connected with geometric topology, combinatorial group theory and surrounding areas.

Air Force research resumés

Author: United States. Air Force. Office of Aerospace Research,United States. Air Force. Office of Aerospace Research. Office of Scientific and Technical Information

Publisher: N.A


Category: Technology & Engineering

Page: N.A

View: 8294