Equivariant preimage theory for G-maps

Authors

• Thaís F.M. Monis, Universidade Estadual Paulista "Júlio de Mesquita Filho"
• Peter Wong, Bates CollegeFollow

Publication Title

Algebraic and Geometric Topology

Document Type

Article

Department or Program

Mathematics

Publication Date

4-25-2026

Keywords

Nielsen theory, Borsuk–Ulam type theorem, preimage theory

Abstract

Let X and Y be closed G-manifolds and B⊂Y a closed invariant nonempty subset where G is a finite group. For any G-map f:X→Y and for every subgroup H≤G, we introduce a Nielsen type number N(f^H,B^H) which is a lower bound for the number of connected components of WH-orbits of (f^H)−1(B^H). This theory generalizes existing Nielsen type numbers for various G and B with an application to the Nielsen Borsuk–Ulam theory for the minimal number of coincidences of f(x)=fτ(x) where f:X→Y and τ a free involution on X.

Comments

Original version is available from the publisher at: https://doi.org/10.2140/agt.2026.26.1529

Recommended Citation

Monis, T. F. M., & Wong, P. 2026. "Equivariant preimage theory for G-maps." Algebraic & Geometric Topology 26(4): 1529-1548.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright Note

© 2026 MSP (Mathematical Sciences Publishers)

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Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.