# Publication list for Kapovich, Michael

## Latest Titles

• Base Product Code Keyword List: coll; COLL; coll/63; COLL/63; coll-63; COLL-63
Print Product Code: COLL/63
Online Product Code: COLL/63.E
Title (HTML): Geometric Group Theory
Author(s) (Product display): Cornelia Druţu; Michael Kapovich
Affiliation(s) (HTML): Mathematical Institute, Oxford, United Kingdom; University of California, Davis, CA
Author Misc Blurb: With an appendix by Bogdan Nica
Abstract:

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of geometric group theory is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls.

The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Book Series Name: Colloquium Publications
Volume: 63
Cover Type: Hardcover
Print ISBN-13: 978-1-4704-1104-6
Online ISBN 13: 978-1-4704-4164-7
Print ISSN: 0065-9258
Online ISSN: 0065-9258
Primary MSC: 20; 57
Textbook?: false
Applied Math?: false
Sample?: false
Reference?: false
Electronic Media?: false
SXG Subject: GT; AA
Online Price 1 Label: List
Online Price 1: 135.00
Print Price 1 Label: List
Print Price 1: 135.00
Online Price 2 Label: Individual Member
Online Price 2: 108.00
Print Price 2 Label: Individual Member
Print Price 2: 108.00
Dual Price 1 Label: List
Dual Price 1: 168.75
Dual Price 2 Label: Individual Member
Dual Price 2: 135
Print Outstock Reason: NYP
Print Outstock Reason Avail Date: Expected publication date December 02, 2017
Online Outstock Reason: NYP
Online Outstock Reason Avail Date: Expected publication date December 02, 2017
Print Add to Cart URL: /some/url/at/AMS/COLL-63
Electronic Add to Cart URL: /some/url/at/AMS/COLL-63.E
Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4164-7&pisbn=978-1-4704-1104-6&epc=COLL/63.E&ppc=COLL/63&title=Geometric%20Group%20Theory&author=Cornelia%20Drutu%3B%20Michael%20Kapovich&type=R

Graduate students and researchers interested in geometric group theory.

Cover Image URL: ~~FreeAttachments/coll-63-cov.jpg
• Base Product Code Keyword List: memo; MEMO; memo/192; MEMO/192; memo-192; MEMO-192; memo/192/896; MEMO/192/896; memo-192-896; MEMO-192-896
Print Product Code: MEMO/192/896
Online Product Code: MEMO/192/896.E
Title (HTML): The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra
Author(s) (Product display): Michael Kapovich; Bernhard Leeb; John J. Millson
Affiliation(s) (HTML): University of California, Davis, Davis, CA; Universität München, Munich, Germany; University of Maryland, College Park, MD
Abstract:

In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $$\mathbb{Q}$$ and its complex Langlands' dual. The authors give a new proof of the “Saturation Conjecture” for $$GL(\ell)$$ as a consequence of their solution of the corresponding “saturation problem” for the Hecke structure constants for all split reductive algebraic groups over $$\mathbb{Q}$$.

Book Series Name: Memoirs of the American Mathematical Society
Publication Month and Year: 2008-02-15
Page Count: 83
Cover Type: Softcover
Print ISBN-13: 978-0-8218-4054-2
Online ISBN 13: 978-1-4704-0502-1
Print ISSN: 0065-9266
Online ISSN: 0065-9266
Primary MSC: 22; 20
Secondary MSC: 14
Textbook?: False
Applied Math?: False
Electronic Media?: False