What question did this study set out to answer?

This research aims to construct a self map on cofiber that induces an equivalence in equivariant theory under specific group conditions.

January 21, 2026Bulletin of the London Mathematical Society0 citationsOpen Access

Equivariant v1, 0v₁, ₀‐self maps

WBWilliam Balderrama YHYueshi Hou SZShangjie Zhang

Key Points

This research aims to construct a self map on cofiber that induces an equivalence in equivariant theory under specific group conditions.
Constructed self map on cofiber of the group
Analyzed conditions based on sizes of the cyclic and quaternion groups
Explored the implications for equivariant theory and geometric fixed points
Established that the self maps are transchromatic
Showed that the self maps lift classical self maps
Indicated the potential for nonzero rational geometric fixed points in the telescope.

Abstract

Abstract Let be a cyclic ‐group or generalized quaternion group, be a virtual ‐set, and be a fixed point free complex ‐representation. Under conditions depending on the sizes of , , and , we construct a self map on the cofiber of which induces an equivalence in ‐equivariant ‐theory. These are transchromatic ‐self maps, in the sense that they are lifts of classical ‐self maps for which the telescope can have nonzero rational geometric fixed points.

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