Integer valued polynomials in topology and number theory

拓扑和数论中的整数值多项式

• 批准号: 8829-2011
• 负责人: Johnson, Keith
• 金额: $ 0.73万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568617
• 关键词: Integer; valued; polynomials; topology; number

This research project investigates algebras of integer valued polynomials and their applications in algebraic topology and number theory. The central objects of study, algebras of polynomials determined by integrality conditions, have been of interest to algebraists for at least 100 years and have been a rich source of examples and structural results. Their occurence in algebraic topology and number theory is more recent, dating from the 1970's, and motivates the study of their computational properties. In this project methods for constructing regular bases for such algebras are developed and these will be used to assist in the computations of stable homotopy groups in topology and of rings of endomorphisms of formal groups in number theory.

该研究项目研究整数值多项式的代数及其 代数拓扑和数论中的应用。研究的中心对象， 由完整性条件确定的多项式代数引起了人们的兴趣 代数学家至少 100 年以来一直是示例和结构的丰富来源 结果。它们在代数拓扑和数论中的出现是最近的，可以追溯到 20 世纪 70 年代，并激发了对其计算特性的研究。在这个项目中 开发了为此类代数构造常规基的方法，并且这些方法将被 用于协助计算拓扑和环中的稳定同伦群 数论中形式群的自同态。