By Armand Borel
Noncompact symmetric and in the community symmetric areas evidently seem in lots of mathematical theories, together with research (representation idea, nonabelian harmonic analysis), quantity thought (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In so much purposes it will be significant to shape a suitable compactification of the gap. The literature facing such compactifications is huge. the most function of this e-book is to introduce uniform structures of many of the identified compactifications with emphasis on their geometric and topological structures.
The publication is split into 3 elements. half I reports compactifications of Riemannian symmetric areas and their mathematics quotients. half II is a learn of compact tender manifolds. half III stories the compactification of in the community symmetric spaces.
Familiarity with the idea of semisimple Lie teams is believed, as is familiarity with algebraic teams outlined over the rational numbers in later components of the publication, even supposing lots of the pertinent fabric is recalled as awarded. another way, the ebook is a self-contained reference geared toward graduate scholars and study mathematicians attracted to the purposes of Lie concept and illustration concept to assorted fields of mathematics.
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