Related papers: Isotopy versus equivariant isotopy in dimensions t…

Any two homologous surfaces of the same genus embedded in a smooth 4-manifold X with simply-connected complements are shown to be smoothly isotopic in the connected sum of X and the product of a 2-sphere with itself, if the surfaces are…

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…

This paper addresses several isotopy problems on $4$-manifolds. First, we classify the isotopy classes of embeddings of $\Sigma$ in $\Sigma\times S^2$ that are geometrically dual to $\{\mbox{pt}\}\times S^2$, where $\Sigma$ is a closed…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties,…

In this note we give a complete obstruction for two homotopic embeddings of a 2-sphere into a 5-manifold to be isotopic. The results are new even though the methods are classical, the main tool being the elimination of double points via a…

We prove that if two closed, connected, regular cosymplectic manifolds have isomorphic groups of cosymplectomorphisms (as topological groups), then the underlying manifolds are diffeomorphic. The proof proceeds by characterizing the Reeb…

Let $(M,g)$ be a $C^\infty$-smooth, $n$-dimensional Riemannian manifold which is diffeomorphic to $\RR^n$ and admit an action of a properly discontinuous and cocompact group. This work proves the existence of a $C^\infty$ equivariant…

A smooth map between manifolds is said to be \emph{image simple} if its restriction to its singular point set is a topological embedding. We study the parity of the number of connected components of the singular point set for image simple…

A diffeomorphism $f$ of a compact manifold $X$ is pseudo-isotopic to the identity if there is a diffeomorphism $F$ of $X\times I$ which restricts to $f$ on $X\times 1$, and which restricts to the identity on $X\times 0$ and $\partial…

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

Let $\mathcal{F}$ be a foliation with a "singular" submanifold $B$ on a smooth manifold $M$ and $p:E \to B$ be a regular neighborhood of $B$ in $M$. Under certain "homogeneity" assumptions on $\mathcal{F}$ near $B$ we prove that every leaf…

For Hamiltonian circle actions on compact, connected, four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as an algebra over the equivariant cohomology of a point. This…

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply…

An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and…

Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly isotopic to the identity. As an application, we give the first…

We introduce a topological invariant, it a type of a graph-manifold, which takes natural values. For a 4-dimensional graph-manifold, whose type does not exceed two, it is proved that its universal cover is bi-Lipschitz equivalent to a…

We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension $n\neq5$, and finite fundamental group, up to foliated diffeomorphism. In addition, we…

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain…