Related papers: Nonsmoothable involutions on spin 4-manifolds

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…

We study finite group actions on smooth manifolds of the form $M\#\Sigma$, where $\Sigma$ is an exotic $n$-sphere and $M$ is a closed aspherical space form. We give a classification result for free actions of finite groups on $M\#\Sigma$…

Let $W$ be a compact smooth $4$-manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the…

The main result of this paper asserts that if a Seifert fibered 4-manifold has nonzero Seiberg-Witten invariant, the homotopy class of regular fibers has infinite order. This is a nontrivial obstruction to smooth circle actions; as…

Let $M^4$ be a smooth compact manifold with a free circle action generated by a vector field $X.$ Then for any invariant symplectic form $\omega$ on $M$ the contracted form $\iota_X \omega$ is nondegenerate. Using the map $\omega -->…

In this article we prove that, if $X$ is a smooth $4$-manifold containing an embedded double node neighborhood, all knot surgery $4$-manifolds $X_K$ are mutually diffeomorphic to each other after a connected sum with $\mathbb{CP}^2$. Hence,…

We construct an infinite family of mutually non-diffeomorphic irreducible smooth structures on the topological 4-manifold $S^2 \times S^2$.

We build a non-compact, orientable, hyperbolic four-manifold of finite volume that does not admit any spin structure.

We say that a topological $n$-manifold $N$ is a cubical $n$-manifold if it is contained in the $n$-skeleton of the canonical cubulation $\mathcal{C}$ of ${\mathbb{R}}^{n+k}$ ($k\geq1$). In this paper, we prove that any closed, oriented…

We prove necessary and sufficient conditions for the existence of non-trivial Steenrod actions on the mod-$2$ cohomology of 4-dimensional toric orbifolds. As applications, the stable homotopy type and the gauge groups of a $4$-dimensional…

Let N be a closed, connected, smooth 4-manifold with H_1(N;Z)=0. Our main result is the following classification of the set E^7(N) of smooth embeddings N->R^7 up to smooth isotopy. Haefliger proved that the set E^7(S^4) with the connected…

Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S^2 x S^2's. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic, provided a certain…

For a compact connected Lie group $G$ acting as isometries on a compact orientable Riemannian manifold $M^{n+1},$ and cohomogeneity not equal to 0 or 2, we prove the existence of a nontrivial embedded $G$-invariant minimal hypersurface,…

A 2018 paper by A. Levine and T. Lidman outlines a proof of the following interesting result in topology of manifolds: there is a compact smooth 4-manifold $W$ with boundary such that $W$ is homotopy equivalent to $S^2$ but there does not…

This paper contains several results concerning circle action on almost-complex and smooth manifolds. More precisely, we show that, for an almost-complex manifold $M^{2mn}$(resp. a smooth manifold $N^{4mn}$), if there exists a partition…

It is well known that for any exotic pair of simply connected closed oriented 4-manifolds, one is obtained from the other by twisting a compact contractible submanifold via an involution on the boundary. By contrast, here we show that for…

Let $X$ be a smooth, compact, oriented $4$-manifold. Building upon work of Li-Liu, Ruberman, Nakamura and Konno, we consider a families version of Seiberg-Witten theory and obtain obstructions to the existence of certain group actions on…

We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy…

We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and give its applications to intersection forms with local coefficients of 4-manifolds. The first application is an analogue of Froyshov's results on…

We prove a surgery formula for the ordinary Seiberg-Witten invariants of smooth $4$-manifolds with $b_1 =1$. Our formula expresses the Seiberg-Witten invariants of the manifold after the surgery, in terms of the original Seiberg-Witten…