Non-simply connected symplectic fillings of lens spaces

TL;DR

This paper investigates the relationship between the fundamental group and second Betti number in minimal symplectic fillings of lens spaces, unifying previous results and revealing connections involving Fibonacci numbers.

Contribution

It provides new unified results linking fundamental groups and Betti numbers in symplectic fillings of lens spaces, extending prior fragmented findings.

Findings

Established bounds relating fundamental group and Betti number

Unified multiple previous results in the literature

Identified a connection involving Fibonacci numbers

Abstract

We prove results exploring the relationship between the fundamental group and the second Betti number of minimal symplectic fillings of lens spaces. These results unify and generalize several disparate facts appearing in the literature. The Fibonacci numbers make a cameo appearance.