Hyperbolic geometry and homotopic homeomorphisms of surfaces

被引：3

作者：

Cantwell, John ^{[1
]}

Conlon, Lawrence ^{[2
]}

机构：

[1] St Louis Univ, Dept Math, St Louis, MO 63103 USA

[2] Washington Univ, Dept Math, St Louis, MO 63130 USA

来源：

GEOMETRIAE DEDICATA | 2015年 / 177卷 / 01期

关键词：

Hyperbolic surface; Homeomorphism; Homotopy; Isotopy; End; CURVES;

D O I：

10.1007/s10711-014-9975-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Epstein-Baer theory of curve isotopies is basic to the remarkable theorem that homotopic homeomorphisms of surfaces are isotopic. The groundbreaking work of R. Baer was carried out on closed, orientable surfaces and extended by D. B. A. Epstein to arbitrary surfaces, compact or not, with or without boundary and orientable or not. We give a new method of deducing the theorem about homotopic homeomorphisms from the results about homotopic curves via the hyperbolic geometry of surfaces. This works on all but 13 surfaces where ad hoc proofs are needed.

引用

页码：27 / 42

页数：16

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