Topological complexity sequences of groups

Summary · qwen2.5:32b

The article defines the topological complexity sequence for groups based on their Milnor constructions, providing an intrinsic refinement that applies to groups with infinite cohomological dimensions. This sequence is shown to be weakly increasing and unbounded for such groups. For a finite group of even order, the asymptotic behavior of this sequence has been determined.

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Exploring topological complexity sequences of groups may have implications for group theory and mathematics. Here's an abstract from a recent publication that discusses this topic.

Excerpt

arXiv:2604.27514v3 Announce Type: replace Abstract: We define the topological complexity sequence of a group as the sequence of topological complexities of its Milnor constructions. This sequence may be regarded as an intrinsic refinement of the topological complexity of a group and, unlike topological complexity itself, is meaningful for groups of infinite cohomological dimension. We show that the topological complexity sequence of every group of infinite cohomological dimension is weakly increasing and unbounded. We then estimate its growth and determine its asymptotic behavior for a finite group of even order.