Normal surfaces in non-compact 3-manifolds

Normal surfaces in topologically finite 3–manifolds

This paper investigates normal surface theory in topologically finite 3–manifolds with ideal triangulations. Treated are closed and non– compact normal surfaces, the projective solution space and the projective admissible solution space, as well as the leaf spaces of the transversely measured singular codimension–one foliations defined by admissible solutions. AMS Classification 57M25, 57N10

Normal Cr Structures on Compact 3-manifolds

We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotiens of S or of a circle bundle over a Riemann surface of positive genus. In the latter case, we prove that their CR automorphisms group is a finite extension of...

Finding Non-Orientable Surfaces in 3-Manifolds

We investigate the complexity of finding an embedded non-orientable surface of Euler genus g in a triangulated 3-manifold. This problem occurs both as a natural question in low-dimensional topology, and as a first non-trivial instance of embeddability of complexes into 3-manifolds. We prove that the problem is NP-hard, thus adding to the relatively few hardness results that are currently known ...

Contractible Open 3-manifolds Which Non-trivially Cover Only Non-compact 3-manifolds

Non-compact Symplectic Toric Manifolds

The paradigmatic result in symplectic toric geometry is the paper of Delzant that classifies compact connected symplectic manifolds with effective completely integrable torus actions, the so called (compact) symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the torus; its image is a simple unim...