Publication list for Kapovich, Michael

Latest Titles

  • Geometric Group Theory
    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
    Copyright Year: 2017
    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
    Home Page?: true
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: 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 March 24, 2017
    Online Outstock Reason: NYP
    Online Outstock Reason Avail Date: Expected publication date March 24, 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
    Readership:

    Graduate students and researchers interested in geometric group theory.

    Cover Image URL: ~~FreeAttachments/coll-63-cov.jpg
  • The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra
    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
    Copyright Year: 2008
    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
    Apparel or Gift: False
    SXG Subject: GT
    Online Price 1 Label: List
    Online Price 1: 65.00
    Print Price 1 Label: List
    Print Price 1: 65.00
    Online Price 2 Label: Individual Member
    Online Price 2: 39.00
    Print Price 2 Label: Individual Member
    Print Price 2: 39.00
    Print Add to Cart URL: /some/url/at/AMS/MEMO-192-896
    Electronic Add to Cart URL: /some/url/at/AMS/MEMO-192-896.E
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-0502-1&pisbn=978-0-8218-4054-2&epc=MEMO/192/896.E&ppc=MEMO/192/896&title=The%20Generalized%20Triangle%20Inequalities%20in%20Symmetric%20Spaces%20and%20Buildings%20with%20Applications%20to%20Algebra&author=Michael%20Kapovich%3B%20Bernhard%20Leeb%3B%20John%20J.%20Millson&type=R