Volume growth via real Lagrangians in Milnor fibers of Brieskorn polynomials

TL;DR

This paper investigates volume growth in Milnor fibers of Brieskorn polynomials, establishing uniform lower bounds using Floer homology and real Lagrangians, advancing understanding of symplectic topology.

Contribution

It introduces a method to estimate volume growth via real Lagrangians and Smith inequalities, providing new bounds in the context of Milnor fibers.

Findings

Established uniform lower bounds for volume growth

Connected real Lagrangians topology to join construction

Applied Smith inequality in wrapped Floer homology

Abstract

In this paper we study the volume growth in the component of fibered twists in Milnor fibers of Brieskorn polynomials. We obtain a uniform lower bound of the volume growth for a class of Brieskorn polynomials using a Smith inequality for involutions in wrapped Floer homology. To this end, we investigate a family of real Lagrangians in those Milnor fibers whose topology can be systematically described in terms of the join construction.