Related papers: Finite type invariants of 3-manifolds
This paper E3 shows how to construct the simplest Exotic Invariant in the simplest way.
On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Buehler and Christian Blanchet we extended his…
This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.
We study a class of 3-dimensional paracontact metric manifolds and we revise some of the results obtain in \cite{SS}.
We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.
This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.
This work surveys classical and recent advances around the existence of exotic differentiable structures on spheres and its connection to stable homotopy theory.
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…
We give a 3-page description of the Gassner invariant / representation of braids / pure braids, along with a description and a proof of its unitarity property.
We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration $\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned by isotopy classes of…
The fundamental groups of most (conjecturally, all) closed 3-manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting…
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…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
We discuss invariants in equivariant birational geometry.
We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.
In this note we give a closed formula for Faltings' delta-invariant of a hyperelliptic Riemann surface.
In this article, we continue the classification of finite type Gauss map surfaces in the Euclidean 3-space E3 with respect to the first fundamental form by studying a subclass of tubes, namely the anchor rings. We show that anchor rings are…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
This note mainly studies the generic finiteness of \phi_m of a complex projective 3-fold of general type. A new result on the classification to bicanonical pencil for Gorenstein 3-folds is attached in the last section.