Related papers: 3-manifolds that can be made acyclic

We characterize the groups of branched twist spins of classical knots in terms of 3-manifold groups, and also give a purely algebraic, conjectural characterization in terms of $PD_3$-groups. We show also that each group is the group of at…

We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering $m$-fold cyclic branched covers with $m$ a prime power, this extension provides new knot concordance…

We establish a lower bound on the complexity orientable locally orientable geometric 3-orbifolds in terms of Delzant's T-invariants of their orbifold-fundamental groups, generalizing previously known bounds for complexity of 3-manifolds.

We introduce eight versions of cyclic homology of a mixed complex and study their properties. In particular, we determine their behaviour with respect to Chen iterated integrals.

We show that $3$-graphs on $n$ vertices whose codegree is at least $(2/3 + o(1))n$ can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing…

A Circumconic passes through a triangle's vertices. We define the Circumbilliard, a circumellipse to a generic triangle for which the latter is a 3-periodic. We study its properties and associated loci.

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 explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

We compute the $p$-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free $S^1$-action. Using this, we show that any non-singular linking pairing on a finite abelian group with homogeneous…

We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry;…

We show that the Membership Problem for finitely generated subgroups of 3-manifold groups is solvable.

We prove that a continuum $X$ is tree-like (resp. circle-like, chainable) if and only if for each open cover $\U_4=\{U_1,U_2,U_3,U_4\}$ of $X$ there is a $\U_4$-map $f:X\to Y$ onto a tree (resp. onto the circle, onto the interval). A…

We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.

We establish a correspondence between trisections of smooth, compact, oriented $4$--manifolds with connected boundary and diagrams describing these trisected $4$--manifolds. Such a diagram comes in the form of a compact, oriented surface…

A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and…

A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We…

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to…

We construct a sequence of geodesics on the modular surface such that the complement of the canonical lifts to the unit tangent bundle are arithmetic 3-manifolds.

We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of…

We classify all connected $n$-dimensional complex manifolds admitting an effective action of the unitary group $U_n$ by biholomorphic transformations. One consequence of this classification is a characterization of ${\bf C}^n$ by its…