The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to ge…
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The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups…
Many of the results originally due to Springer, Veldkamp, Jacobson, Suh, and others on octonion planes are derived here in a uniform fashion, valid for all characteristics and for both split and division octonion algebras, by using an exceptional quadratic Jordan algebra. Among …
Groups which satisfy commutator relations of the type satisfied by Chevalley groups, called here "groups with Steinberg relations", are shown to have certain nonassociative division algebras as parameters. This, in turn, allows an introduction of coordinates into certain polygon…
Using concepts from valuation theory, we obtain a characterization of all collinearity-preserving functions from one affine or projective Desarguesian plane into another. The case in which the planes are projective and the range contains a quadrangle has been treated previously …
"The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry." "The primary focus of the book is on transformations of the plane. The transformational point of view…
Measurement is all around us - from the circumference of a pizza to the square footage of an apartment, from the length of a newborn baby to the number of miles between neighboring towns. Whether inches or miles, centimeters or kilometers, measures of distance stand at the very …
Measurement is all around us - from the circumference of a pizza to the square footage of an apartment, from the length of a newborn baby to the number of miles between neighboring towns. Whether inches or miles, centimeters or kilometers, measures of distance stand at the very …
This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homolog…
