Special Surfaces in Knot Complements

Tomova 的研究重点是 3 维流形的 Heegaard 分裂和流形结的桥面。 给定封闭 3 歧管中的结，桥表面是将歧管分解为手柄体并将结切割成简单弧的表面。在过去的一年半中，托莫娃证明了有关桥梁表面行为的几个重要结果。她打算扩展和推广她的成果，并将她的工作应用于该领域的几个开放性问题。随着 DNS 分子的发现和最近弦理论的出现，纽结的研究已经走到了现代科学的最前沿。结理论是拓扑学的一个分支，研究打结弦的特性，也是 Maggy Tomova 的主要兴趣领域。她对结的研究还需要理解 3 流形，即局部看起来像 3 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.