Deh s algorithm for simple diagrams

作者：Frohman Charles^*; Kania Bartoszynska Joanna

来源：Journal of Knot Theory and Its Ramifications, 2015, 24(14): 1550074.

DOI：10.1142/S0218216515500741

• Simple diagrams
• triangulation
• punctured surface

Dehn gave an algorithm for deciding if two cyclic words in the standard presentation of the fundamental group of a closed oriented surface of positive genus represent the same conjugacy class. A simple diagram on a surface is a disjoint union of simple closed curves none of which bound a disk. If F is a once punctured closed surface of negative Euler characteristic, simple diagrams are classified up to isotopy by their geometric intersection numbers with the edges of an ideal triangulation of F. Simple diagrams on the unpunctured surface F can be represented by simple diagrams on F. The weight of a simple diagram is the sum of its geometric intersection numbers with the edges of the triangulation. We show that you can pass from any representative to a least weight representative via a sequence of elementary moves, that monotonically decrease weights. This leads to a geometric analog of Dehn's algorithm for simple diagrams.

• 出版日期2015-12
• 单位国家自然科学基金委员会