Isotropic immersions

Minimal Lagrangian isotropic immersions in indefinite complex space forms

On the Moduli of Isotropic and Helical Minimal Immersions between Spheres

DoCarmo-Wallach theory and its subsequent refinements assert the rich abundance of spherical minimal immersions, minimal immersions of round spheres into round spheres. A spherical minimal immersion can be written as a conformal minimal immersion f : Sm → SV with domain the Euclidean m-sphere Sm and range the unit sphere SV of a Euclidean vector space V . Takahashi’s theorem then implies that t...

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 ...

Invariants of Generic Immersions

An immersion of a smooth manifold M into a smooth manifold W is a smooth map with everywhere injective differential. Two immersions are regularly homotopic if they can be connected by a continuous 1-parameter family of immersions. An immersion is generic if all its self-intersections are transversal. In the space F of immersions M → W , generic immersions form an open dense subspace. Its comple...