Related papers: A 3-Manifold with no Real Projective Structure

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general…

This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let $X$ be a smooth projective real algebraic 3-fold. Assume that the set of real points is an…

In a previous paper the second author showed that if $M$ is a pseudomanifold with complementarity other than the 6-vertex real projective plane and the 9-vertex complex projective plane, then $M$ must have dimension $\geq 6$, and - in case…

We prove that a complete hyperbolic 3-manifold of finite volume does not admit a properly embedded noncompact surface of finite topology with constant mean curvature greater than or equal to 1.

Let M be a compact oriented irreducible 3-manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that the fundamental group of M is virtually special.

We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperk\"ahler manifolds). We show that they are either totally real fields or number fields generated by Salem numbers. This is unlike…

A normal pseudomanifold is a pseudomanifold in which the links of simplices are also pseudomanifolds. So, a normal 2-pseudomanifold triangulates a connected closed 2-manifold. But, normal $d$-pseudomanifolds form a broader class than…

We introduce a new obstruction to the existence of a universal $0$-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of $0$-cycles is representable but which…

Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.

We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, that such spaces are homeomorphic to connected sums of some…

We introduce a class of one-ended open 3-manifolds which can be `recursively' defined from two compact 3-manifolds, and construct examples of manifolds in this class which fail to have a toric decomposition in the sense of Jaco-Shalen and…

We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…

In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space…

We prove a structure theorem for 3-manifolds with non-trivial JSJ-decomposition and 2-generated fundamental group. We deduce a variety of Corollaries. Note this is not a complete classification of such manifolds. In particular we believe…

For a noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to $\mathbb{R}^3$ or the universal cover splits. As a corollary, it confirms a conjecture of Milnor in dimension 3.

The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynomials and sums of squares on a real variety. We survey the…

This is an expository proof that, if $M$ is a compact $n$-manifold with no boundary, then the set of holonomies of strictly-convex real-projective structures on $M$ is a subset of $\operatorname{Hom}(\pi_1M,\operatorname{PGL}(n+1,\mathbb…

We prove that any mapping torus of a closed 3-manifold has zero simplicial volume. When the fiber is a prime 3-manifold, classification results can be applied to show vanishing of the simplicial volume, however the case of reducible fibers…

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…

We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R^3. We also provide examples of minimal vertex triangulations of closed, connected, orientable…