Homology 3-spheres, homology cobordism, and contractible 4-manifolds

A central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. In this talk, we address this problem for plumbed 3-manifolds and we present the classical and new results together. Along the way, we touch symplectic geometry by using the classical results of Eliashberg and Gompf.
This problem is naturally linked to the algebraic structure of the homology cobordism group. We also give several families of plumbed 3-manifolds generating infinite rank summands in this group.
Our method and approach are based on Kirby calculus, Mazur's argument, its generalization, Ozsváth-Szabó $d$-invariant, and involutive Heegaard Floer homology.
Zoom 889 7525 9254 (new channel), without password.