Related papers: Six-dimensional GKM manifolds with four fixed poin…

Kreck's modified surgery gives an approach to classifying smooth $2n$-manifolds up to stable diffeomorphism, i.e. up to connected sum with copies of $S^n \times S^n$. In dimension 4, we use a combination of modified and classical surgery to…

We establish three major fixed-point theorems for functions satisfying an odd power type contractive condition in G-metric spaces. We first consider the case of a single mapping, followed by that of a triplet of mappings and we conclude by…

In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…

We show that if G is a 4-critical graph embedded in a fixed surface $\Sigma$ so that every contractible cycle has length at least 5, then G can be expressed as $G=G'\cup G_1\cup G_2\cup ... \cup G_k$, where $|V(G')|$ and $k$ are bounded by…

We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these…

This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed, oriented, smooth manifold or a simply connected 5-dimensional closed, smooth manifold. We…

In this article, we show the existence of conjugations on many simply-connected spin 6-manifolds with free integral cohomology. In a certain class the only condition on X^6 to admit a conjugation with fixed point set M^3 is the obvious one:…

We reduce M-theory on a G_2 orbifold with co-dimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional…

We study a class of fourth order geometric equations defined on a 4-dimensional compact Riemannian manifold which includes the Q-curvature equation. We obtain sharp estimates on the difference near the blow-up points between a bubbling…

Let $P$ be a set of $n$ points in general position in the plane. Given a convex geometric shape $S$, a geometric graph $G_S(P)$ on $P$ is defined to have an edge between two points if and only if there exists an empty homothet of $S$ having…

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…

Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling construction to 2-complexes over certain finite abelian groups…

In an earlier paper we explained how to convert the problem of symplectically embedding one 4-dimensional ellipsoid into another into the problem of embedding a certain set of disjoint balls into \CP^2 by using a new way to desingularize…

In the paper, we investigate properties of the nine-dimensional variety of the inflection points of the plane cubic curves. The description of local monodromy groups of the set of inflection points near singular cubic curves is given. Also,…

We prove that there is an action of the cyclic group $\mathbf{C}_2$ on the $10$-dimensional Floyd manifold which turns it into a conjugation manifold. The submanifold of fixed points is the $5$-dimensional Floyd manifold, whose cohomology…

The aim of this note is to provide a comprehensive treatment of the homotopy theory of $\Gamma$-$G$-spaces for $G$ a finite group. We introduce two level and stable model structures on $\Gamma$-$G$-spaces and exhibit Quillen adjunctions to…

Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$. We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the existence of almost complex blow-ups at $x$ under suitable assumptions on the almost…

For an equivariantly formal action of a compact torus $T$ on a smooth manifold $X$ with isolated fixed points we investigate the global homological properties of the graded poset $S(X)$ of face submanifolds. We prove that the condition of…

The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its…

Consider the blow-up $X$ of $\mathbb{P}^3$ at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism $\phi_X$ on $X$, induced by the complete linear system of a divisor of…