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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 especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.

Homology theory. --- Cobordism theory. --- Differential topology --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Cobordism theory --- Homology theory --- Homologie

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Traditionally the Adams-Novikov spectral sequence has been a tool which has enabled the computation of generators and relations to describe homotopy groups. Here a natural geometric description of the sequence is given in terms of cobordism theory and manifolds with singularities. The author brings together many interesting results not widely known outside the USSR, including some recent work by Vershinin. This book will be of great interest to researchers into algebraic topology.

Cobordism theory. --- Manifolds (Mathematics) --- Singularities (Mathematics) --- Adams spectral sequences. --- Adams-Novikov spectral sequences --- Novikov spectral sequences, Adams --- -Spectral sequences (Mathematics) --- Geometry, Algebraic --- Geometry, Differential --- Topology --- Differential topology --- Cobordism theory --- SINGULARITIES (Mathematics) --- Adams spectral sequences

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MEMS Vibratory Gyroscopes provides a solid foundation in the theory and fundamental operational principles of micromachined vibratory rate gyroscopes, and introduces structural designs that provide inherent robustness against structural and environmental variations. In part one, the dynamics of the vibratory gyroscope sensing element is developed, common micro-fabrication processes and methods commonly used in inertial sensor production are summarized, design of mechanical structures for both linear and torsional gyroscopes are presented, and electrical actuation and detection methods are discussed along with details on experimental characterization of MEMS gyroscopes. In part two, design concepts that improve robustness of the micromachined sensing element are introduced, supported by constructive computational examples and experimental results illustrating the material. MEMS Vibratory Gyroscopes is a must have book for engineers in both industry and academia who specialize in the design and manufacture of gyroscopes. Readers will find: A unique balance between theory and practical design issues. Comprehensive and detailed information outlining the mathematical models of the mechanical structure and system-level sensor design. Solid background Information on mechanical and electrical design, fabrication, packaging, testing and characterization. About The MEMs Reference Shelf: "The MEMs Reference Shelf is a series devoted to Micro-Electro-Mechanical Systems (MEMs) which combine mechanical, electrical, optical, or fluidic elements on a common microfabricated substrate to create sensors, actuators, and microsystems. The series, authored by leading MEMs practitioners, strives to provide a framework where basic principles, known methodologies and new applications are integrated in a coherent and consistent manner." STEPHEN D. SENTURIA Massachusetts Institute of Technology, Professor of Electrical Engineering, Emeritus.

Cobordism theory. --- Differentiable mappings. --- Topological transformation groups. --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- Gyroscopes. --- Microelectromechanical systems. --- MEMS (Microelectromechanical systems) --- Micro-electro-mechanical systems --- Micro-machinery --- Microelectromechanical devices --- Micromachinery --- Micromachines --- Micromechanical devices --- Micromechanical systems --- Gyros (Gyroscopes) --- Gyroscope --- Engineering. --- Mechanical engineering. --- Automotive engineering. --- Electronics. --- Microelectronics. --- Electronic circuits. --- Electronics and Microelectronics, Instrumentation. --- Circuits and Systems. --- Automotive Engineering. --- Mechanical Engineering. --- 51 --- 51 Mathematics --- Mathematics --- Mathematical analysis --- Electromechanical devices --- Microtechnology --- Mechatronics --- Rotational motion (Rigid dynamics) --- Tops --- Systems engineering. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Construction --- Industrial arts --- Technology --- Engineering systems --- System engineering --- Industrial engineering --- System analysis --- Electrical engineering --- Physical sciences --- Design and construction --- Algebraic topology --- Topologie algébrique --- Transformation groups --- Transformations, Groupes de --- Electron-tube circuits --- Electric circuits --- Electron tubes --- Electronics --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Semiconductors --- Miniature electronic equipment --- Lie, Groupes de --- Géometrie différentielle --- Algebraic topology. --- Transformation groups. --- Géometrie différentielle --- Topologie algébrique --- Variétés topologiques --- Topologie differentielle --- Analyse harmonique