On fillings of homotopy equivalent contact structures

TL;DR

This paper introduces a topological approach to filling contact structures on connected sums of S^2×S^3, demonstrating the existence of non-symplectomorphic strong fillings for homotopy equivalent contact structures with zero first Chern class.

Contribution

It presents a novel topological method for filling contact structures and constructs examples of distinct strong fillings on homotopy equivalent manifolds.

Findings

Existence of non-symplectomorphic strong fillings

Construction of examples on connected sums of S^2×S^3

Homotopy equivalent contact structures with vanishing first Chern class

Abstract

This paper provides a topological method for filling contact structures on the connected sums of $S^2\times S^3$. Examples of nonsymplectomorphic strong fillings of homotopy equivalent contact structures with vanishing first Chern class on $\#_k S^2\times S^3$ $(k\geq2)$ are produced.