# Spine removal surgery and the geography of symplectic fillings

## TL;DR

This paper establishes universal bounds on the Euler characteristic and signature of minimal symplectic fillings for certain contact 3-manifolds using a novel spine removal surgery technique.

## Contribution

It introduces a new application of spine removal surgery to bound topological invariants of symplectic fillings in contact geometry.

## Key findings

- Universal bounds on Euler characteristic and signature for specified contact 3-manifolds.
- Application of spine removal surgery to symplectic topology.
- Demonstrates the effectiveness of the new surgery technique in bounding invariants.

## Abstract

We prove that for any contact 3-manifold supported by a spinal open book decomposition with planar pages, there is a universal bound on the Euler characteristic and signature of its minimal symplectic fillings. The proof is an application of the spine removal surgery operation recently introduced in joint work of the authors with Van Horn-Morris.