Related papers: Symplectized Torelli mapping tori

Following McDuff and Tolman's work on toric manifolds [McDT06], we focus on 4-dimensional NEF toric manifolds and we show that even though Seidel's elements consist of infinitely many contributions, they can be expressed by closed formulas.…

Let $S_g$ be a closed, oriented surface of genus $g$, and let $\operatorname{Mod}(S_g)$ denote its mapping class group. The Torelli group $\mathcal{I}_g$ is the subgroup of $\operatorname{Mod}(S_g)$ consisting of mapping classes that act…

We exhibit a finitely generated group $\M$ whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface $\su$ of infinite genus, and…

We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…

Let X be a complete toric variety of dimension n and \del the fan in a lattice N associated to X. For each cone \sigma of \del there corresponds an orbit closure V(\sigma) of the action of complex torus on X. The homology classes…

We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which…

An effective class in a closed symplectic four-manifold $(X, \omega)$ is a two-dimensional homology class which is realized by a $J$-holomorphic cycle for every tamed almost complex structure $J$. We prove that effective classes are…

We compute the Lagrangian Floer cohomology groups of certain tori in closed simply connected symplectic 4-manifolds arising from Fintushel-Stern knot surgery. These manifolds are usually not symplectically aspherical. As a result of the…

We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some…

In this paper we prove that the Torelli part of the symplectomorphism groups of the $n$-point ($n\leq 4$) blow-ups of the projective plane is trivial. Consequently, we determine the symplectic mapping class group. It is generated by…

In this paper, we study Morse functions with regular level sets consisting of spheres, tori, or Klein Bottles on $3$-dimensional closed manifolds. We characterize $3$-dimensional manifolds represented by connected sums each of whose…

In the definition of irreducible holomorphic symplectic manifolds the condition of being simply connected can be replaced by vanishing irregularity. We discuss finite quotients X of complex tori where the space of reflexive 2-forms is…

We consider the Euler characteristics $\chi(M)$ of closed orientable topological $2n$-manifolds with $(n-1)$-connected universal cover and a given fundamental group $G$ of type $F_n$. We define $q_{2n}(G)$, a generalized version of the…

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite…

It is the purpose of this paper to construct families of examples of nonsymplectic 4-manifolds which (up to sign) have just one Seiberg-Witten basic class.

We introduce machinery to allow ``cut-and-paste''-style inductive arguments in the Torelli subgroup of the mapping class group. In the past these arguments have been problematic because restricting the Torelli group to subsurfaces gives…

A Euclidean minimal torus with planar ends gives rise to an immersed Willmore torus in the conformal 3--sphere $S^3=\R^3\cup \{\infty\}$. The class of Willmore tori obtained this way is given a spectral theoretic characterization as the…

We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg-Witten simple type. This result shows that there exists a large class of topological 4-manifolds such that all smooth structures have…