Subgroups and Combinatorial Nonpositive Curvature

子群和组合非正曲率

• 批准号: RGPIN-2018-04453
• 负责人: Wise, Daniel
• 金额: $ 5.1万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759169
• 关键词: Subgroups; Combinatorial; Nonpositive; Curvature

The proposed research circulates around the principal investigator's deep interest in cubical geometry and its applications.Highlights of the proposal include the following:1) A genuinely new proof of the Malnormal Special Quotient Theorem.2) An explicit characterization of the class of groups that are virtually limit groups.3) A cubulation result for full relatively hyperbolic amalgams.3) A new and more general form of nonpositively curvature for square complexes.4) A concrete and explicit virtual cubulation theorem for 3-manifolds.5) A proposal to prove that irreducibilty is generic for cocompact lattices in the products of trees.6) An investigation of virtual algebraic fibering for special cube complexes beyond that obtained in the 3-manifold setting.7) A continued search for a unified theory of coherence.9) An exploration of growth-gaps.

拟议的研究围绕着主要研究者对立方几何及其应用的浓厚兴趣展开。该提案的亮点包括以下内容：1）反常特殊商定理的真正新证明。2）对以下群的类别的明确表征虚拟限制群。3) 完全相对双曲汞齐的立方结果。3) 平方复形的非正曲率的新且更一般的形式。4) 具体且明确的虚拟立方定理3-流形。5) 证明不可约性对于树的乘积中的协紧格子是通用的提议。6) 对特殊立方体复合体的虚拟代数纤维的研究超出了在 3-流形设置中获得的结果。7) 继续搜索统一的一致性理论。9）对增长差距的探索。