Special Surfaces in Knot Complements

Tomova的研究集中在三维流形的高度分裂和流形中结的桥表面。给定封闭3-歧管中的一个结，桥接面是一个将歧管分解成把手体并将结切割成简单弧线的表面。在过去的一年半里，托莫娃已经证明了几个关于桥梁表面行为的重要结果。她打算扩展和概括她的结果，并将她的工作应用于该领域的几个开放问题。随着DNS分子的发现和弦理论的出现，对结的研究已经走到了现代科学的前沿。结理论是研究结弦性质的拓扑学的一个分支，也是Maggy Tomova的主要研究方向。她对结的研究也需要了解三维流形，局部看起来像三维空间的物体。

Tomova's research centers on Heegaard splittings of 3-dimensional manifolds and bridge surfaces for knots in manifolds. Given a knot in a closed 3-manifold, a bridge surface is a surface that decomposes the manifold into handlebodies and also cuts the knot into simple arcs. In the last year and a half Tomova has proven several important results about the behavior of bridge surfaces. She intends to extend and generalize her results and apply her work to several open problems in the area.With the discovery of the DNS molecule and the recent advent of string theory, the study of knots has come to the forefront of modern science. Knot Theory is a subarea of Topology which studies the properties of knotted strings and is the main area of interest of Maggy Tomova. Her study of knots also requires an understanding of 3-manifolds, objects that locally look like 3-dimensional space.