Analytic subdivision invariants

Subdivisions and transgressive chains

Combinatorial transgressions are secondary invariants of a space admitting triangulations. They arise from subdivisions and are analogous to transgressive forms such as those arising in Chern-Weil theory. Unlike combinatorial characteristic classes, combinatorial transgressions have not been previously studied. First, this article characterizes transgressions that are path-independent of subdivision sequence. The result is obtained by using a cohomology on posets that is shown to be equivalent to higher derived functors of the inverse (or projective) limit over the opposite poset. Second, a ca…

Analytic invariants of boundary links

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.

Delta invariant of curves on rational surfaces I. The analytic approach

We prove that if (C,0) is a reduced curve germ on a rational surface singularity (X,0) then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair (X,C). Furthermore, we also identify it with another (a priori) embedded analytic invariant, which is motivated by the theory of adjoint ideals. Finally, we connect our formulae with the local correction term at singular points of the global Riemann--Roch formula, valid for projective normal surfaces, introduced by Blache.

G₂流形的一个解析不变量

An analytic invariant of G_2 manifolds

本文通过构造显式例子证明闭7-流形上G₂-和乐度量模空间通常不连通，定义整数取值的ν-不变量解析细化检测分支，并计算了特定扭曲连通和的不变量。