arXiv subjects

Tatyana Khodorovskiy

Publications and source records attributed to Tatyana Khodorovskiy.

3 recordsLinked to original sources

arXiv2013

Bounds on Embeddings of Rational Homology Balls in Symplectic 4-manifolds

The rational homology balls $B_n$ appeared in Fintushel and Stern's rational blow-down construction [FS2]. Later, Symington [Sy1], defined this operation in the symplectic category. In [Kh2], the author defined the inverse procedure, the symplectic rational blow-up. In this paper, we study the obstructions to symplectically rationally blowing up a symplectic 4-manifold, i.e. the obstructions to symplectically embedding the rational homology balls $B_n$ into a symplectic 4-manifold. We prove a theorem and give additional examples which suggest that in order to symplectically embed the rational homology balls $B_n$, for high n, a symplectic 4-manifold must at least have a high enough $c_1^2$ as well.

math.SG↗

arXiv2013

Symplectic Rational Blow-up

Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres $C_n$ is replaced with a rational homology ball $B_n$, $n \geq 2$. Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic $C_n$ (given by symplectic spheres) is replaced by a symplectic copy of $B_n$ to yield a new symplectic manifold. As a result, a symplectic rational blow-down can be performed on a manifold whenever such a configuration of symplectic spheres can be found. In this paper, we define the inverse procedure, the rational blow-up in the symplectic category, where we present the symplectic structure of $B_n$ as an entirely standard symplectic neighborhood of a certain Lagrangian 2-cell complex. Consequently, a symplectic rational blow-up can be performed on a manifold whenever such a Lagrangian 2-cell complex is found.

math.SG↗

arXiv2012

Smooth Embeddings of Rational Homology Balls

The rational homology balls $B_n$ appeared in Fintushel and Stern's rational blow-down construction [FS] and were subsequently used (e.g. Fintushel-Stern[FS4], Park[Pa2]) to construct exotic smooth manifolds with small Euler numbers. We show that a large class of smooth 4-manifolds have all of the $B_n$'s for odd $n \geq 3$ embedded in them. In particular, we give explicit examples, using Kirby calculus, of several families of smooth embeddings of the rational homology balls $B_n$.

math.GT↗