数学科学系讲座:Vanishing Cycles of Matrix Singularities

活动

活动详情

  • 时间: 10:30-11:30
  • 日期: Friday 6th December
  • 地点: MA305
  • 主讲人: Professor Victor Goryunov

活动简介

The talk will start with a recollection of Milnor’s classical result on the local topology of isolated singularities of holomorphic functions: a local non- critical level of such a function is homotopic to a wedge of spheres of the middle dimension. According to Brieskorn, the spheres can be realised as those vanishing at Morse critical points of a small generic perturbation of the function.

The main objects of the talk will be holomorphic map germs

M :(Cs,0) → Matn,

where the target is the space of either square, or symmetric, or skew- symmetric n × n matrices. The target contains the set ∆ of all degenerate matrices, and we will be interested in the vanishing topology of M−1(∆). Our attention is on the singular Milnor fibre of M, that is, the local inverse image V of ∆ under a generic small perturbation of M. The variety V is highly singular, but, according to Lˆe and Siersma, it is still homotopic to a wedge of (s − 1)-dimensional spheres.

The aim of the talk is to describe local models for the spheres vanishing in the matrix context.