Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving nece...

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Bibliographic Details

Main Author:	Mühlherr, Bernhard (Author)
Format:	Electronic eBook
Language:	English
Published:	Princeton Princeton University Press 2015
Series:	Annals of Mathematics Studies v.1
Subjects:	Algebraic topology Buildings (Group theory) Combinatorial geometry Group theory Gebäude > Mathematik
Summary:	Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings
Item Description:	Description based on publisher supplied metadata and other sources
Physical Description:	1 online resource (353 pages)
ISBN:	9781400874019