Mathematical Sciences: Equivariant Homology Interpretation of the Invariant Defined by Bieri-Strebel-Neuman-Renz

这个项目涉及到导出某些不变量 与元阿贝尔的有限表示相关， 可解群 这些不变量已被证明有许多 与数论、代数几何和拓扑学的联系。 不变量使人们能够局部地描述 具有一个有限的艾伦伯格.麦克莱恩空间直到一个固定的维数。 在本提案中，主要研究者将研究这些 使用等变同源性的不变量。 这种方法将统一 这个理论出现在交换代数和拓扑学中， 同时，也提供了对理论的更好理解。

This project is concerned with deriving certain invariants associated with the finite presentation of metabelian and solvable groups. These invariants have been shown to have many connections with number theory, algebraic geometry and topology. The invariants enable one to describe locally the property of having a finite Eilenberg.MacLane space up to a fixed dimension. In this proposal the principal investigator will study these invariants using equivariant homology. This approach will unify this theory as it appears in commutative algebra and in topology, as well as, provide a better understanding of the theory.