Brieskorn spheres, homology cobordism and homology balls

Brieskorn spheres Σ(p,q,r) represent a special class of 3-manifolds which are defined to be links of singularities x^p y^q z^r=0. Over the years, they have been main objects for the understanding of the algebraic structure of the integral homology cobordism group. In this talk, we will present several families of Brieskorn spheres which do or do not bound integral and rational homology balls via Ozsváth-Szabó d-invariant, involutive Heegaard Floer homology, and Kirby calculus. We will investigate their positions in both integral and rational homology cobordism groups.

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