Related papers: Non-orientable 3-manifolds of surface-complexity o…

We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic (n+1)-orbifold.

Using the invariant algebra of the reflection group denoted by $G\_{32}$ in Shephard-Todd classification, we construct three irreducible surfaces in $P^3$ with many singularities: one of them has degree $24$ and contains $1440$ quotient…

We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle.…

We show that fundamental groups of compact, orientable, irreducible 3-manifolds with toroidal boundary are Grothendieck rigid.

Taubes proved that all compact oriented four-manifolds admit non-flat instantons. We show that there exists a non-compact oriented four-manifold having no non-flat instanton.

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains…

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first…

The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the…

A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…

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 give a concrete example of an infinite sequence of $(p_n, q_n)$-lens spaces $L(p_n, q_n)$ with natural triangulations $T(p_n, q_n)$ with $p_n$ taterahedra such that $L(p_n, q_n)$ contains a certain non-orientable closed surface which is…

A trisection of a smooth, closed, oriented 4-manifold is a decomposition into three 4-dimensional 1-handlebodies meeting pairwise in 3-dimensional 1-handlebodies, with triple intersection a closed surface. The fundamental groups of the…

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of…

We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume,…

We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface in X and an unknotted projective plane in a 4-sphere. This…

We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in…

Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to $s$-cobordism by their $w_2$-type, equivariant intersection form and the Kirby-Siebenmann…

We show that the classification up to homeomorphism of closed topological nonorientable 4-manifolds with fundamental group of order 2 due to Hambleton-Kreck-Teichner can be used to classify a large set of such 4-manifolds with cyclic…

We give a criterion on a group $\pi$ and a homomorphism $w \colon \pi \to C_2$ under which closed $4$-manifolds with fundamental group $\pi$ and orientation character $w$ are classified up to homotopy equivalence by their quadratic…

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is…