A 3-Manifold with no Real Projective Structure

We show that the connected sum of two copies of real projective 3-space does not admit a real projective structure. This is the first known example of a connected 3-manifold without a real projective structure.Comment: Minor corrections suggested by refere

Finite-volume Hyperbolic 3-Manifolds contain immersed Quasi-Fuchsian surfaces

The paper contains a new proof that a complete, non-compact hyperbolic $3$-manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface.Comment: Final version to appear in AGT. Some typos corrected, particularly def (3.6). Rewording of 4 paragraphs in proof of (4.2) for added clarity. Final section added comparing this paper to the approach of Masters and Zhan

Three-manifolds, virtual homology, and group determinants

We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3-manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology carried by the solid tori used for Dehn-filling. The polynomial is a symmetrized form of the group determinant studied by Frobenius and Dedekind. As a corollary every such hyperbolic 3-manifold has infinitely many virtually Haken Dehn-fillings.Comment: This is the version published by Geometry & Topology on 29 November 200