Compressed surface charge coordinates

This module owns the three real coordinates and the real and imaginary parts of the (s,t) surface charge. It contains no wall equation or geometric realization.

@[reducible, inline]

abbrev CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.NumClass : Type

A compressed numerical surface class (r, c, d).

Equations

• CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.NumClass = (ℝ × ℝ × ℝ)

def CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.NumClass.rk (v : NumClass) : ℝ

The rank coordinate.

Equations

• v.rk = v.1

def CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.NumClass.deg (v : NumClass) : ℝ

The degree coordinate.

Equations

• v.deg = v.2.1

def CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.NumClass.ch2 (v : NumClass) : ℝ

The integrated second Chern-character coordinate.

Equations

• v.ch2 = v.2.2

noncomputable def CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.reZ (s t : ℝ) (v : NumClass) : ℝ

The real part of the twisted surface charge at (s,t).

Equations

• CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.reZ s t v = -v.ch2 + s * v.deg - s ^ 2 / 2 * v.rk + t ^ 2 / 2 * v.rk

def CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.imZ (s t : ℝ) (v : NumClass) : ℝ

The imaginary part of the twisted surface charge at (s,t).

Equations

• CategoryTheory.Triangulated.WeakStabilityCondition.StabilityCondition.Wall.imZ s t v = t * (v.deg - s * v.rk)