Splittings of Free Groups, Normal Forms and Partitions of Ends

Proceedings Mathematical Sciences

Suhas Pandit¹  Siddhartha Gadgil² 

[1] Department of Mathematics, Indian Institute of Science Education and Research, Pune 0, India$$;Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$

关键词: Free groups;    sphere complex;    algebraic intersection numbers;    graphs of trees.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Splittings of a free group correspond to embedded spheres in the 3-manifold $M=sharp_k S^2× S^1$. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in $𝜋_2(M)$ can be represented by an embedded sphere.

【 授权许可】

Unknown