Conjecture on the sequential topological complexity of quaternionic space forms

Let Q8mQ_{8m} denote the generalized quaternion group of order 8m8m acting freely on S3S^3, and let rr-th sequential topological complexity be denoted by TCr\mathsf{TC}_r. Sequential topological complexity conjecture. For m≥1m\ge 1, the rr-th sequential topological complexity of S3/Q8mS^3/Q_{8m} is equal to 3r3r.

This conjecture concerns the growth of higher topological complexity for spherical space forms and would provide an affirmative instance of the rationality behavior asked about for sequential topological complexity. Its resolution is not stated in the source.

References

Primary source

Yuki Minowa, “On the topological complexity of non-simply connected spaces”, arXiv:2603.09407 (2026).

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