Hyperbolic geometry and homotopic homeomorphisms of surfaces

Hyperbolic geometry and homotopic homeomorphisms of surfaces
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双曲几何和曲面的同伦同胚

DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
L. Conlon
L. Conlon
中科院分区：
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文献类型：
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作者：
J. Cantwell;L. Conlon

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Epstein-Baer的曲线同位素理论是曲面的同伦同胚是同位素这一著名定理的基础。R. Baer是在封闭的可定向曲面上进行的，并由D. B。A. Epstein的任意曲面，紧或不紧，有或没有边界和定向或没有。利用曲面的双曲几何，给出了由同伦曲线的结果导出同伦同胚定理的一种新方法。除了13个需要特别证明的表面外，这对所有表面都有效。
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.