Splittings of free groups, normal forms and partitions of ends

被引：3

作者：

Gadgil, Siddhartha ^{[1
]}

Pandit, Suhas ^{[2
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Indian Inst Sci Educ & Res, Dept Math, Pune 411021, Maharashtra, India

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2010年 / 120卷 / 02期

关键词：

Free groups; sphere complex; algebraic intersection numbers; graphs of trees; GEOMETRIC INTERSECTION-NUMBERS; AUTOMORPHISM-GROUPS; COMPLEX; SURFACES; CURVES; DIMENSION; STABILITY; OUT(F-N); HOMOLOGY; TREES;

D O I：

10.1007/s12044-010-0020-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x 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 pi (2)(M) can be represented by an embedded sphere.

引用

页码：217 / 241

页数：25

共 31 条

[1]

[Anonymous], 2001, ALGEBRAIC TOPOLOGY

[2] The Tits alternative for out(Fn) I:: Dynamics of exponentially-growing automorphisms [J].