Euler obstruction of essentially isolated determinantal singularities

行列式奇点上 $1$-形式的欧拉障碍

The Euler obstruction of a $1$-form on a determinantal singularity

研究行列式奇点背景下局部欧拉障碍与 $1$-形式的 Poincaré-Hopf-Nash 指数之间的联系，并应用于计算具有刚性奇点的 IDS 上原点处分层孤立奇点函数的欧拉障碍。

Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes on these varieties. We give explicit formulas of their Chern-Schwartz-MacPherson classes and Chern-Mather classes via standard Schubert calculus. As corollaries we obtain formulas for their (generic) sectional Euler characteristics, characteristic cycles and polar classes.

Controlled surgery and $\mathbb{L}$-homology

This paper presents an alternative approach to controlled surgery obstructions. The obstruction for a degree one normal map $(f,b): M^n \rightarrow X^n$ with control map $q: X^n \rightarrow B$ to complete controlled surgery is an element $σ^c (f, b) \in H_n (B, \mathbb{L})$, where $M^n, X^n$ are topological manifolds of dimension $n \geq 5$. Our proof uses essentially the geometrically defined $\mathbb{L}$-spectrum as described by Nicas (going back to Quinn) and some well known homotopy theory. We also outline the construction of the algebraically defined obstruction, and we explicitly describ…