Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants

TL;DR

This paper proves that the symplectic mapping class groups of many K3 surfaces are infinitely generated, using Seiberg-Witten invariants instead of Floer theory, providing new insights into symplectic topology.

Contribution

It introduces a novel approach to studying symplectic mapping class groups of K3 surfaces via Seiberg-Witten invariants, avoiding Floer-theoretic methods.

Findings

Symplectic mapping class groups of many K3 surfaces are infinitely generated.

Seiberg-Witten invariants can be used to analyze symplectic mapping class groups.

The approach bypasses Floer-theoretic machinery, simplifying certain analyses.

Abstract

The purpose of this note is to prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated. Our proof makes no use of any Floer-theoretic machinery but instead follows the approach of Kronheimer and uses invariants derived from the Seiberg-Witten equations.