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Sasakian Geometry$
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Charles Boyer and Krzysztof Galicki

Print publication date: 2007

Print ISBN-13: 9780198564959

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198564959.001.0001

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Links as Sasakian Manifolds

Links as Sasakian Manifolds

(p.299) Chapter 9 Links as Sasakian Manifolds
Sasakian Geometry

Charles P. Boyer

Krzysztof Galicki

Oxford University Press

This chapter is devoted to the geometry of links of isolated hypersurface singularities, as well as a review of the differential topology of homotopy spheres a la Kervaire and Milnor. The differential topology of links is a beautiful piece of mathematics, and the chapter offers a hands-on ‘user's guide’ approach with much emphasis on the famous work of Brieskorn in determining the difieomorphism types of certain homotopy spheres. This includes a presentation of the well known Brieskorn graph theorem as well as the geometry of Brieskorn-Pham links. When the singularities arise from weighted homogeneous polynomials, the links have a natural Sasakian structure with either definite (positive or negative) or null basic first Chern class. Emphasis is given to the positive case which corresponds to having positive Ricci curvature.

Keywords:   Brieskorn-Pham links, Brieskorn graph theorem, difieomorphism type, difierential topology, isolated hypersurface singularities, links, homotopy spheres, Kervaire-Milnor group, positive Sasakian links, positive Ricci curvature

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