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This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham's theorem on simplicial complexes. In addition, Sullivan's results on computing the rational homotopy type from forms is presented.

New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch...

The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is...

The description for this book, Topics in Transcendental Algebraic Geometry. (AM-106), Volume 106, will be forthcoming.

The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974.

In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order.

Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the...

This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham s theorem on simplicial complexes. In addition, Sullivan s results on computing the rational homotopy type from forms is presented.

New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch...