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.

- 开发用于识别表面，结和三维空间的实用算法。这些对于实验非常有用 并了解此类问题的计算复杂性。 - 了解在恒定负曲率的3维空间中最小表面的特性，并应用了结的复杂性和这些空间的结构。 - 开发一个四维空间的理论 欧几里得4空间。由于Freedman-Quinn的强大方法不适用于大多数此类空间，因此将使用新技术。