Planar surface immersions

Visual Contours and Planar Sections for Affine Immersions

In this paper we consider planar sections and visual contours of co-dimension one affine immersions. The main theorem says that the third order Taylor expansion of the difference between the visual contour and planar section functions is exactly the cubic form. We also consider parameterizations on two dimensional affine immersions whose coordinate lines are geodesics, in one direction, and bot...

Excluding Graphs as Immersions in Surface Embedded Graphs

We prove a structural characterization of graphs that forbid a fixed graph H as an immersion and can be embedded in a surface of Eüler genus γ. In particular, we prove that a graph G that excludes some connected graph H as an immersion and is embedded in a surface of Eüler genus γ has either “small” treewidth (bounded by a function of H and γ) or “small” edge connectivity (bounded by the maximu...

Poincaré Immersions

We show that the fundamental theorem of immersion theory admits a Poincaré duality space analogue. Along the way, we obtain new homotopy theoretic proofs of the existence and uniqueness of the Spivak normal fibration of a closed Poincaré space.

Induced Immersions

A graph G contains a multigraph H as an induced immersion if H can be obtained from G by a sequence of vertex deletions and lifts. We present a polynomial-time algorithm that decides for any fixed multigraph H whether an input graph G contains H as an induced immersion. We also show that for every multigraph H with maximum degree at most 2, there exists a constant cH such that every graph with ...

Surface construction from planar contours