Related papers: Vanishing structure set of 3-manifolds

This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These…

We reprove and generalize the result that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a…

This is the less official, English version of the proof of the fact that every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.

This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or…

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic 1-form…

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…

We prove that the second Betti number of a compact Riemannian manifold vanishes under certain Ricci curved restriction.

There is a conjecture that a complete Riemannian 3-manifold with bounded sectional curvature, and pointwise pinched nonnegative Ricci curvature, must be flat or compact. We show that this is true when the negative part (if any) of the…

We prove a relative Kawamata Viehweg vanishing type theorem for birational morphisms. We use this to prove a Grauert Riemenschneider theorem over log canonical threefolds without zero dimensional log canonical centers, in residue…

We study the vanishing of cohomology in triangulated categories admitting a central ring action. In particular, we study vanishing gaps and symmetry.

Looijenga's vanishing theorem on the moduli space of curves $M_g$ says that the tautological ring vanishes above degree $g-2$. We prove an analogous result for the tautological cohomology ring of the moduli space of K3 surfaces.

In this paper, we first give a new simple proof to the elimination theorem of definite fold by homotopy for generic smooth maps of manifolds of dimension strictly greater than $2$ into the $2$--sphere or into the real projective plane. Our…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

We analyze the structure of the algebraic manifolds $Y$ of dimension 3 with $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$, $i>0$ and $h^0(Y, {\mathcal{O}}_Y) > 1$, by showing the deformation invariant of some open surfaces. Secondly, we show…

Let M^7 a manifold with holonomy in G_2, and Y^3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that M_{X,Y}, the moduli space of its associative deformations with boundary in the fixed…

We show a special case of Steenbrink vanishing for rational singularities in positive characteristic. As a consequence, we prove that strongly $F$-regular threefolds and klt threefolds in characteristic $p>41$ satisfy Steenbrink vanishing.

Given a compact oriented triangulated $3$-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used…

Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is…