Medial/Skeletal Linking Structures for Multi-Region Configurations

James Damon, University of North Carolina, Chapel Hill, NC. Ellen Gasparovic, Duke University, Durham, NC.

Introduction
Part 1. Medial/Skeletal Linking Structures: Multi-region configurations in $/mathbb{R}^{n+1}$
Skeletal linking structures for multi-region configurations in ${/mathbb R}^{n+1}$
Blum medial linking structure for a generic multi-region configuration
Retracting the full Blum medial structure to a skeletal linking structure
Part 2. Positional Geometry of Linking Structures: Questions involving positional geometry of a multi-region configuration
Shape operators and radial flow for a skeletal structure
Linking flow and curvature conditions
Properties of regions defined using the linking flow
Global geometry via medial and skeletal linking integrals
Positional geometric properties of multi-region configurations
Part 3. Generic Properties of Linking Structures via Transversality Theorems: Multi-distance and height-distance functions and partial multi-jet spaces
Generic Blum linking properties via transversality theorems
Generic properties of Blum linking structures
Concluding generic properties of Blum linking structures
Part 4. Proofs and Calculations for the Transversality Theorems: Reductions of the proofs of the transversality theorems
Families of perturbations and their infinitesimal properties
Completing the proofs of the transversality theorems
Appendix A. List of frequently used notation
Bibliography.