相关论文: Semistable 3-fold flips

We prove existence of flips for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

We review the construction of the AdS/CFT dressing factor, its analytic properties and several checks of its validity.

We prove the termination of 4-fold canonical flips.

In this paper we show the existence of three dimensional rigid, and thus unfoldable, lattice conformations. The structure we found has 450+ bonds, and we provide a computer assisted proof of the existence of such structures. The existence…

We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…

In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.

This is a latest survey article on embeddings of multibranched surfaces into 3-manifolds.

This is an overview article, based on my 2018 Kinosaki lecture, that surveys and announces work on 3-fold flopping contractions, their affine combinatorics, stability conditions, tilting bundles and autoequivalences. Some first applications…

After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.

We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish-Wallace surgery presentation; one proof uses a refinement due to Kaplan and some basic contact geometry. This complements a…

We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.

This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…

We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two…

We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new…

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of…

We prove the stability under lamination of a set of real, symmetric 3$\times$3 matrices that can be viewed as a subset of the effective conductivities of a polycrystal. Constructed in a companion paper, such set in combination with several…

We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.