Related papers: On the mapping class groups of simply-connected sm…

Let M be a topological manifold modelled on topological vector spaces, which is the union of an ascending sequence of such manifolds M_n. We formulate a mild condition ensuring that the k-th homotopy group of M is the direct limit of the…

We consider a closed odd-dimensional oriented manifold $M$ together with an acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a natural…

We show examples of pairs of smooth, compact, homeomorphic 4-manifolds, whose diffeomorphism types are distinguished by the topology of the singular sets of smooth stable maps defined on them. In this distinction we rely on results from…

Let $N_{g,n}$ denote the nonorientable surface of genus $g$ with $n$ boundary components and $M(N_{g,n})$ its mapping class group. We obtain an explicit finite presentation of $M(N_{g,n})$ for $n=0,1$ and all $g$ such that $g+n>3$.

Let $(X,\omega)$ be a compact symplectic manifold of dimension $2n$ and let $Ham(X,\omega)$ be its group of Hamiltonian diffeomorphisms. We prove the existence of a constant $C$, depending on $X$ but not on $\omega$, such that any finite…

Using the Seiberg-Witten monopole equations, Baraglia recently proved that for most of simply-connected closed smooth $4$-manifolds $X$, the inclusions $\mathrm{Diff}(X) \hookrightarrow \mathrm{Homeo}(X)$ are not weak homotopy equivalences.…

Suppose M is a non-compact connected n-manifold without boundary, DD(M) is the group of C^\infty-diffeomorphisms of M endowed with the Whitney C^\infty-topology and DD_0(M) is the identity connected component of DD(M), which is an open…

We present a rigidity theorem for the action of the mapping class group $\pi_0(\mathrm{Diff}(M))$ on the space $\mathcal{R}^+(M)$ of metrics of positive scalar curvature for high dimensional manifolds $M$. This result is applicable to a…

In this paper, we prove that the group $\mathrm{Aut}_\mathbb{Q}(X)$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds $X$ of general type which either satisfy $q(X)\geq 3$ or have a Gorenstein…

Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…

For every compact almost complex manifold (M,J) equipped with a J-preserving circle action with isolated fixed points, a simple algebraic identity involving the first Chern class is derived. This enables us to construct an algorithm to…

In this work we compute the first integral cohomology of the pure mapping class group of a non-orientable surface of infinite topological type and genus at least 3. To this purpose, we also prove several other results already known for…

Let $X$ be a closed smooth manifold, $G$ be a simple connected compact real Lie group, $M (G)$ be the group of all smooth maps from $X$ to $G$, and $M_0 (G)$ be its connected component for the $\mathcal C^\infty$-compact open topology. It…

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…

In this paper, we first prove that any closed simply connected 4-manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4-manifolds: $\mathbb{S}^4$,…

A family of closed manifolds is called cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. We establish cohomological rigidity for large families of 3-dimensional and…

We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

We consider the space of smooth complex projective plane curves of degree d. Defined over this is the tautological family of plane curves, and hence there is a monodromy representation into the mapping class group of the fiber. We show two…

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology.…