A Geometric Approach To Homology Theory

Author: S. Buonchristiano
Publisher: Cambridge University Press
ISBN: 0521209404
Size: 41.48 MB
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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.

The Poincar Conjecture

Author: James Carlson
Publisher: American Mathematical Soc.
ISBN: 0821898655
Size: 68.66 MB
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The conference to celebrate the resolution of the Poincare conjecture, which is one of the Clay Mathematics Institute's seven Millennium Prize Problems, was held at the Institut Henri Poincare in Paris. Several leading mathematicians gave lectures providing an overview of the conjecture--its history, its influence on the development of mathematics, and, finally, its proof. This volume contains papers based on the lectures at that conference. Taken together, they form an extraordinary record of the work that went into the solution of one of the great problems of mathematics.

Low Dimensional Topology

Author: Samuel J. Lomonaco
Publisher: American Mathematical Soc.
ISBN: 0821850164
Size: 67.42 MB
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This volume arose from a special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.

Algebraic Varieties

Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Size: 27.54 MB
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An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Sheaf Theory

Author: B. R. Tennison
Publisher: Cambridge University Press
ISBN: 0521207843
Size: 50.23 MB
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Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

Zz 2 Homotopy Theory

Author: Michael Charles Crabb
Publisher: Cambridge University Press
ISBN: 0521280516
Size: 37.69 MB
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This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin-Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest.

Combinatorics

Author: H. N. V. Temperley
Publisher: Cambridge University Press
ISBN: 0521285143
Size: 24.28 MB
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The articles collected here are the texts of the invited lectures given at the Eighth British Combinatorial Conference held at University College, Swansea. The contributions reflect the scope and breadth of application of combinatorics, and are up-to-date reviews by mathematicians engaged in current research. This volume will be of use to all those interested in combinatorial ideas, whether they be mathematicians, scientists or engineers concerned with the growing number of applications.