Related papers: On four-manifolds without 1- and 3-handles

In [HT], two of us constructed a closed oriented 4-dimensional manifold with fundamental group $\Z$ that does not split off $S^1\times S^3$. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth…

Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for…

A smooth four manifold is of finite type $r$ if its Donaldson invariant satisfies D((x^2-4)^r)=0. We prove that every simply connected manifold is of finite type by using the structure of Donaldson invariants in the presence of immersed…

We give necessary and sufficient conditions for a closed smooth 6-manifold N to be diffeomorphic to a product of a surface F and a simply connected 4-manifold M in terms of basic invariants like the fundamental group and cohomological data.…

In this article, we construct countably many mutually non-isotopic diffeomorphisms of some closed non simply-connected 4-manifolds that are homotopic to but not isotopic to the identity, by surgery along $\Theta$-graphs. As corollaries of…

Every 4-dimensional infrasolvmanifold $M$ with $\beta_1(M;\mathbb{Q})>0$ or which is flat or has one of the geometries $\mathbb{N}il^4$, $\mathbb{S}ol_{m,n}^4$, or $\mathbb{S}ol_0^4$ bounds. However there are non-orientable…

In this note, we prove -- in dimension at most 4 -- a conjectue of Hao which says that a morphism $f : X \to A$ to a simple abelian variety $A$ is smooth if and only if there is a 1-form pulled back from A without any zeros. We also give a…

In the present paper we consider class $G$ of orientation preserving Morse-Smale diffeomorphisms $f$, which defined on closed 3-manifold $M^3$, and whose non-wandering set consist of four fixed points with pairwise different Morse indices.…

We classify closed, topological spin$^+$ 4-manifolds with fundamental group $\pi$ of cohomological dimension $\leq 3$ (up to s-cobordism), after stabilization by connected sum with at most $b_3(\pi)$ copies of $S^2\times S^2$. In general we…

For each pair $(e,\sigma)$ of integers satisfying $2e+3\sigma\ge 0$, $\sigma\leq -2$, and $e+\sigma\equiv 0\pmod{4}$, with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic $e$ and…

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.

Let M be a closed, irreducible, genus two 3-manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M. Then each component manifold M_i of M-F has handle number at most one, i.e.…

We develop a framework that generalizes Budney-Gabai's $W_3$ invariant on $\pi_0\textrm{Diff}(S^1\times D^3,\partial)$ to 4-manifolds with 1-handles. As applications, we show that if $M=(S^1\times D^3)\natural \hat M$ where $\hat M$ either…

We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not…

We study the possibility of realizing exotic smooth structures on punctured simply connected $4$-manifolds as leaves of a codimension one foliation on a compact manifold. In particular, we show the existence of uncountably many smooth open…

In this note we prove that a four-dimensional compact oriented half-confor\-mally flat Riemannian manifold $M^4$ is topologically $\mathbb{S}^{4}$ or $\mathbb{C}\mathbb{P}^{2},$ provided that the sectional curvatures all lie in the interval…

We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit space. As an extension of this work we…

We study complete $3$-manifolds with nonnegative scalar curvature under additional regularity assumptions. We prove that a contractible such manifold is diffeomorphic to $\mathbb{R}^3$, and that an open handlebody admitting such a metric…

For every integer g greater than or equal to 2, there exist infinitely many pairwise nonhomeomorphic smooth 4-manifolds that admit genus-g Lefschetz fibrations over S^2 but do not carry any complex structure with either orientation. This…

We give constraints on smooth families of 4-manifolds with boundary using Manolescu's Seiberg-Witten Floer stable homotopy type, provided that the fiberwise restrictions of the families to the boundaries are trivial families of 3-manifolds.…