Edited by: Rob de Jeu, Vrije Universiteit, Amsterdam, The Netherlands, and James D. Lewis, University of Alberta, Edmonton, AB, Canada

Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch

Fields Institute Communications, Volume: 56
2009; 336 pp; hardcover
ISBN-13: 978-0-8218-4494-6
Expected publication date is September 30, 2009.

Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic K-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.

Readership

Graduate students and research mathematicians interested in algebraic geometry, Hodge theory, K-theory, Motives, and algebraic cycles.

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Kenji Fukaya, Kyoto University, Japan, Yong-Geun Oh, University of Wisconsin, Madison, WI, Hiroshi Ohta, Nagoya University, Japan, and Kaoru Ono, Hokkaido University, Sapporo, Japan

Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I

AMS/IP Studies in Advanced Mathematics, Volume: 46
2009; 396 pp; hardcover
ISBN-13: 978-0-8218-4836-4
Expected publication date is October 18, 2009.

This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_infty algebras and A_infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Readership

Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and sting theory.

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Kenji Fukaya, Kyoto University, Japan, Yong-Geun Oh, University of Wisconsin, Madison, WI, Hiroshi Ohta, Nagoya University, Japan, and Kaoru Ono, Hokkaido University, Sapporo, Japan

Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part II

AMS/IP Studies in Advanced Mathematics, Volume: 46
2009; 805 pp; hardcover
ISBN-13: 978-0-8218-4837-1
Expected publication date is October 18, 2009.

This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_infty algebras and A_infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Readership

Graduate students and research mathematicians interested in symplectic geometry, low-dimensional topology, mirror symmetry, and sting theory.

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Stephen Childress, New York University, Courant Institute of Mathematical Sciences, NY

An Introduction to Theoretical Fluid Mechanics

Courant Lecture Notes, Volume: 19
2009; 201 pp; softcover
ISBN-13: 978-0-8218-4888-3
Expected publication date is October 4, 2009.
This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Readership

Graduate students and research mathematicians interested in fluid mechanics.

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