Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities

Links of isolated singularities defined by weighted homogeneous polynomials have a natural Sasakian structure. Since it is known that Sasaki-Einstein metrics have positive Ricci curvature, and since positive Sasakian structures give rise to Sasakian metrics with positive Ricci curvature, it is useful to determine which links have a positive Sasakian structure. This corresponds to the Fano index of the associated weighted projective variety being positive. Links of dimension $2n-1$ are $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\'{a}r, Nakamaye, and others. This paper investigates isolated singularities of codimension 2 complete intersections with 5 dimensional links of positive index and provides a complete list up to degree 600, hence a complete (up to degree 600) list of types of links having positive Sasakian structures.

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics & Statistics

Year

2013

Author dc:creator

• Inbody, Christopher Stuart

Contributors dc:contributor

• Boyer, Charles
• Charles Boyer
• Ivan Cheltsov
• Michael Nakamaye
• Dimiter Vassilev

• Sasakian Structures
• Einstein Metrics
• Weighted Projective Varieties
• Links of Singularities
• Complete Intersections

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/math_etds/21

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:math_etds-1020