Topics on 3- and 4-dimensional manifolds.

有关 3 维和 4 维流形的主题。

• 批准号: DP0208490
• 负责人: Prof Joachim Rubinstein
• 金额: $ 33.06万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0208490
• 关键词: Topics; dimensional; manifolds.

- to develop practical algorithms for recognising surfaces, knots and 3-dimensional spaces. These will be very useful for experimentation and to understand the computational complexity of such questions. - to understand the properties of minimal surfaces in 3-dimensional spaces of constant negative curvature, with applications to the complexity of knots and the structure of these spaces. - to develop a theory of 4-dimensional spaces which are covered by Euclidean 4-space. New techniques will be utilised, since the powerful methods of Freedman-Quinn do not apply to most such spaces.

- 开发实用的算法，用于识别表面，节点和三维空间。这些将是非常有用的实验 并理解这些问题的计算复杂性。 - 了解三维常负曲率空间中极小曲面的性质，并应用于结的复杂性和这些空间的结构。 - 发展了四维空间理论， 欧几里得四维空间新的技术将被利用，因为强大的方法弗里德曼奎因不适用于大多数这样的空间。