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Polar Spaces
 
Hendrik Van Maldeghem Ghent University, Belgium
A publication of European Mathematical Society
Softcover ISBN:  978-3-98547-080-8
Product Code:  EMSMLM/3
List Price: $55.00
AMS Member Price: $44.00
Please note AMS points can not be used for this product
Click above image for expanded view
Polar Spaces
Hendrik Van Maldeghem Ghent University, Belgium
A publication of European Mathematical Society
Softcover ISBN:  978-3-98547-080-8
Product Code:  EMSMLM/3
List Price: $55.00
AMS Member Price: $44.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Münster Lectures in Mathematics
    Volume: 32024; 182 pp
    MSC: Primary 51

    Polar spaces are the natural geometries for the classical groups. Due to the stunning simplicity of an axiom system found by Buekenhout and Shult, they play a central role in incidence geometry and also appear as combinatorial objects in many disciplines, such as discrete mathematics, graph theory, finite geometry, and coding theory. They can also be viewed as a class of spherical Tits buildings and, as such, were classified by Jacques Tits—using pseudo-quadratic forms and octonion algebras. Polar spaces bridge the areas of group theory, algebra, combinatorics and incidence geometry.

    These lecture notes arose from a master’s course in Ghent, Belgium, taught annually between 2010 and 2024. Besides many basic and general geometric properties of polar spaces, the book contains a complete algebraic description of all polar spaces of rank, at least 3 linking them with polarities in projective spaces. The discussion of the related classical groups is limited to the study of axial and central elations. The classification of top-thin polar spaces is included in detail. Triality in top-thin polar spaces of rank 4 is explained both geometrically and algebraically. The last chapter introduces parapolar spaces, which are geometric structures using polar spaces as building blocks. This opens the door for exploring geometries related to the exceptional groups. An appendix explains composition algebras, which are used to describe the so-called non-embeddable polar spaces and triality.

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Researchers and graduate students interested in incidence geometry, in particular, in the theory of polar spaces.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 32024; 182 pp
MSC: Primary 51

Polar spaces are the natural geometries for the classical groups. Due to the stunning simplicity of an axiom system found by Buekenhout and Shult, they play a central role in incidence geometry and also appear as combinatorial objects in many disciplines, such as discrete mathematics, graph theory, finite geometry, and coding theory. They can also be viewed as a class of spherical Tits buildings and, as such, were classified by Jacques Tits—using pseudo-quadratic forms and octonion algebras. Polar spaces bridge the areas of group theory, algebra, combinatorics and incidence geometry.

These lecture notes arose from a master’s course in Ghent, Belgium, taught annually between 2010 and 2024. Besides many basic and general geometric properties of polar spaces, the book contains a complete algebraic description of all polar spaces of rank, at least 3 linking them with polarities in projective spaces. The discussion of the related classical groups is limited to the study of axial and central elations. The classification of top-thin polar spaces is included in detail. Triality in top-thin polar spaces of rank 4 is explained both geometrically and algebraically. The last chapter introduces parapolar spaces, which are geometric structures using polar spaces as building blocks. This opens the door for exploring geometries related to the exceptional groups. An appendix explains composition algebras, which are used to describe the so-called non-embeddable polar spaces and triality.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Researchers and graduate students interested in incidence geometry, in particular, in the theory of polar spaces.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.