Related papers: Finite-type invariants of three-manifolds and the …
This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the…
The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, that is, those that have finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic…
We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P^2-irreducible manifolds with positive first Betti number. For…
We study Tamagawa numbers and other invariants (especially Tate-Shafarevich sets) attached to commutative and pseudo-reductive groups over global function fields. In particular, we prove a simple formula for Tamagawa numbers of commutative…
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
We show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of 3-manifolds. We also prove that if the FIC is…
We show how to construct, starting from a quasi-Hopf algebra, or quasi-quantum group, invariants of knots and links. In some cases, these invariants give rise to invariants of the three-manifolds obtained by surgery along these links. This…
We show that finitely generated and purely pseudo-Anosov subgroups of fibered 3-manifolds with reducible monodromy are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. Combined with results of…
An essential goal in the study of finite type invariants of some objects (knots, manifolds) is the construction of a universal finite type invariant, universal in the sense that it contains all finite type invariants of the given objects.…
We define and study refined Gopakumar-Vafa invariants of contractible curves in complex algebraic 3-folds, alongside the cohomological Donaldson--Thomas theory of finite-dimensional Jacobi algebras. These Gopakumar-Vafa invariants can be…
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random…
In this paper, we prove the Novikov conjecture for a class of highly non-linear groups, namely discrete subgroups of the diffeomorphism group of a compact smooth manifold. This removes the volume-preserving condition in a previous work.…
In this paper, we discuss relations among several invariants of 3-manifolds including Meyer's function, the eta-invariant, the von Neumann rho-invariant and the Casson invariant from the viewpoint of the mapping class group of a surface.
In this paper, we show that the Turaev-Viro invariant volume conjecture posed by Chen and Yang is preserved under gluings of toroidal boundary components for a family of $3$-manifolds. In particular, we show that the asymptotics of the…
We continue to develop an obstruction theory for embedding 2-spheres into 4-manifolds in terms of Whitney towers. The proposed intersection invariants take values in certain graded abelian groups generated by labelled trivalent trees, and…
We explain how it is possible to study $\mathrm{U}\!\left(1\right)$ BF theory over a connected closed oriented smooth $3$-manifold in the formalism of path integral thanks to Deligne-Beilinson cohomology. We show how we can…
Futaki invariants of the classical moduli space of 4d N=1 supersymmetric gauge theories determine whether they have a conformal fixed point in the IR. We systematically compute the Futaki invariants for a large family of 4d N=1…
Let $\pi$ be a group satisfying the Farrell-Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincar\'e duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$…
The main theorem shows that if M is an irreducible compact connected orientable 3-manifold with non-empty boundary, then the classifying space BDiff(M rel dM) of the space of diffeomorphisms of M which restrict to the identity map on…