arXiv research

The simplicial volume of non-R^3 contractible 3-manifolds is infinite.

Article proves contractible 3-manifolds with positive scalar curvature are homeomorphic to R^3.

Uncountably many contractible 3-manifolds with double 3-space property and those without are identified.

Survey of recent scalar curvature results on open 3-manifolds.

Groups can embed uniformly but not act properly on contractible manifolds.

New proof of contractibility of metrics on 3-manifolds.

Study shows no complete positive scalar curvature for certain 3-manifolds.

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…

3-manifolds and handlebody interiors with nonnegative scalar curvature are topologically rigid.

Study shows contractibility of certain metrics on 3-manifolds.

3-manifolds with positive scalar curvature and bounded geometry are contractible.

The paper constructs contractible manifolds with knotted spheres.

We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold $M$ is at least the weight of $π(M, \ast)$. This lower bound is sharp for the 3-m…

Finite type for 3-manifolds with boundary.

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object S(W) called the simplicial complex of minimal R^2-irreducible end reductions of …

Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of M is isomorphic to a subgroup of the group Aut(S(W)) of simplicial automorphism…

Paper tackles which 3-spheres bound contractible 4-manifolds or homology 4-balls.

The paper proves the Generalized Smale Conjecture and contractibility of moduli spaces.

Given a genus two Heegaard splitting for a non-prime 3-manifold, we define a special subcomplex of the disk complex for one of the handlebodies of the splitting, and then show that it is contractible. As applications, first we show that the complex of Haken spheres for the splitting is contractible, which refines the r…

The study of double coset growth in specific groups confirms a conjecture about generic 3-manifolds.

The paper shows that certain 3-manifolds are essentially Euclidean space.

Motivated by a recent paper of Gabai on the Whitehead contractible 3-manifold, we investigate contractible manifolds $M^n$ which decompose or split as $M^n = A \cup_C B$ where $A,B,C \approx \mathbb{R}^n$ or $A,B,C \approx \mathbb{B}^n$. Of particular interest to us is the case $n=4.$ Our main results exhibit large col…

The paper shows a 3D shape can't fit into certain compact spaces.

Study on 3-manifolds with nonnegative scalar curvature and positive harmonic functions.

New proofs of h-principles in contact 3-manifolds.

Contractibility of tight contact structures on $S^3$ proven.

Study of 3-manifolds with non-trivial boundary groups, showing they cannot be corks.

This is a "software upgrade" to a paper originally published in 1976, with cleaner statements and improved proofs. The main result is that, in a Haken 3-manifold, the space of all incompressible surfaces in a single isotopy class is contractible, except when the surface is the fiber of a surface bundle structure, in wh…

The paper studies invariant metrics with positive scalar curvature on 3-manifolds.

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G=π_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\widetilde{M}$ of $M$ must be \homeo\ to $\RRR$. This has been verified directly under several different additional assumptions on $G…

The study examines 3-manifolds with slow scalar curvature decay and finds Whitehead manifold properties.

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 3-manifold M, the inclusion from the isometry group of M to the diffeomorphism group of M…

The paper shows how to transform certain 3D shapes into hyperbolic ones.

New algorithms deform and contract discrete manifolds into spheres.

A new flow method reduces Lorentz contraction to a simple algebraic decay.

Study of contractible manifolds and their twists to determine if they are $S^4$.

A unique hyperbolic metric is found for each spherical cone-metric on the boundary of a hyperbolizable 3-manifold.

TQFT invariants are either easy or hard to compute, depending on the TQFT type.

We show that every orientable 3-manifold is a classifying space BΓwhere Γis a groupoid of germs of homeomorphisms of R. This follows by showing that every orientable 3-manifold M admits a codimension one foliation F such that the holonomy cover of every leaf is contractible. The F we construct can be taken to be C^1 bu…

About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed manifold, Mostow rigidity assures that a hyperbolic structure is unique when it ex…

Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain approximations to the diagonal are constructed, and explicit contracting homotopies…

New example shows noncontractible fiberings for a 3-manifold.

Paper proves a relative version of coarse Alexander duality and applies it to Jordan cycles.

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F is two if F is topologically minimal.

Proves Calabi-Yau theorem for certain nonnegative curvature manifolds.

The Kakimizu complex is usually defined in the context of knots, where it is known to be quasi-Euclidean. We here generalize the definition of the Kakimizu complex to surfaces and 3-manifolds (with or without boundary). Interestingly, in the setting of surfaces, the complexes and the techniques turn out to replicate th…

On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if bdry V is nonempty, then the Reeb vector field R is transverse to …

Reeb flow made transverse to foliations without invariant measures.