A simple closure condition for the normal cone intersection formula

A general intersection formula for Lagrangian cycles

We prove a generalization to the context of real geometry of an intersection formula for the vanishing cycle functor, which in the complex context is due to Dubson, Lê, Ginsburg and Sabbah (after a conjecture of Deligne). It is also a generalization of similar results of Kashiwara-Schapira, where these authors work with a suitable assumption about the micro-support of the corresponding construc...

The Intersection R-Torsion for Finite Cone

Torsion invariants were originally introduced in the 3-dimensional setting by K. Reidemeister [23] in 1935 who used them to give a homeomorphism classification of 3-dimensional lens spaces. The Reidemeister torsions (R-torsions for short) are defined using linear algebra and combinational topology. The salient feature of R-torsions is that it is not a homotopy invariant but rather a simple homo...

A sufficient normality condition for Turing's formula

Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

Let Γ := {x ∈ R | q(x) ∈ Θ}, where q : R → R is a twice continuously differentiable mapping, and Θ is a nonempty polyhedral convex set in R. In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping NΓ : R ⇒ R, x 7→ NΓ(x), under the condition that Mq(x) := q(x) − Θ is metrically subregular at the reference point. Then, based on this fo...

Intersection of a Triangle and a Cone