5-15【林剑锋】Monodromy of Milnor fibrations detected by Seiberg-Witten theory

This talk discusses recent applications of mathematical gauge theory in singularity theory.

Milnor's fibration theorem is a landmark in singularity theory, allowing us to use topological method to study local behavior of analytic functions near their critical points. In complex dimension 3, the Milnor fibration gives an open book decomposition of S^5. And the monodromy is diffeomorphism on the Milnor fiber. When the Milnor fibration is given by a weighted homogeneous polynomial, the algebraic monodromy (i.e. the monodromy induced map on homology) is always of finite order. We will sketch a proof that, except for the ADE singularities, this monodromy is of infinite order in the smooth mapping class group. Our proof makes uses of recent advances in equivariant Seiberg-Witten-Floer theory. I will discuss the motivation of this problem (simultaneous resolution of ADE singularities by Aityah, Brieskorn and Wahl) and further applications in low dimensional topology. (Based on a joint with Hokuto Konno, Anubhav Mukherjee and Juan Munoz Echaniz).