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Equivariant preimage theory for $G$-maps

Thaís F M Monis and Peter Wong

Algebraic & Geometric Topology 26 (2026) 1529–1548
DOI: 10.2140/agt.2026.26.1529
Bibliography
1 P E Conner, E E Floyd, Differentiable periodic maps, 33, Springer (1964) MR176478
2 F S Cotrim, D Vendrúscolo, Nielsen coincidence theory applied to Borsuk–Ulam geometric problems, Topology Appl. 159 (2012) 3738 MR2991948
3 F S Cotrim, D Vendrúscolo, The Nielsen Borsuk–Ulam number, Bull. Belg. Math. Soc. Simon Stevin 24 (2017) 613 MR3743265
4 R Dobreńko, The obstruction to the deformation of a map out of a subspace, Dissertationes Math. (Rozprawy Mat.) 295 (1990) 29 MR1082410
5 R Dobreńko, Z Kucharski, On the generalization of the Nielsen number, Fund. Math. 134 (1990) 1 MR1071257
6 E Fadell, S Husseini, An ideal-valued cohomological index theory with applications to Borsuk–Ulam and Bourgin–Yang theorems, Ergodic Theory Dynam. Systems 8 (1988) 73 MR967630
7 O Frolkina, Minimizing the number of Nielsen preimage classes, from: "The Zieschang Gedenkschrift" (editors M Boileau, M Scharlemann, R Weidmann), Geom. Topol. Monogr. 14, Geom. Topol. Publ. (2008) 193 MR2484704
8 D L Gonçalves, The Borsuk–Ulam theorem for surfaces, Quaest. Math. 29 (2006) 117 MR2209795
9 D L Gonçalves, J Guaschi, V C Laass, The Borsuk–Ulam property for homotopy classes of self-maps of surfaces of Euler characteristic zero, J. Fixed Point Theory Appl. 21 (2019) 65 MR3947929
10 D L Gonçalves, J Guaschi, V C Laass, The Borsuk–Ulam property for homotopy classes of maps from the torus to the Klein bottle, Topol. Methods Nonlinear Anal. 56 (2020) 529 MR4235703
11 D L Gonçalves, J Guaschi, V C Laass, The Borsuk–Ulam property for homotopy classes of maps from the torus to the Klein bottle, II, Topol. Methods Nonlinear Anal. 60 (2022) 491 MR4563245
12 D L Gonçalves, J Guaschi, V C Laass, Free cyclic actions on surfaces and the Borsuk–Ulam theorem, Acta Math. Sin. (Engl. Ser.) 38 (2022) 1803 MR4506748
13 D L Gonçalves, A P dos Santos, Diagonal involutions and the Borsuk–Ulam property for product of surfaces, Bull. Braz. Math. Soc. 50 (2019) 771 MR3993193
14 D Gonçalves, P Wong, Cohomology of preimages with local coefficients, Algebr. Geom. Topol. 6 (2006) 1471 MR2253456
15 K Y Ha, J B Lee, Preimage homomorphism indices of preimage classes, Topology Appl. 293 (2021) 107555 MR4229462
16 J Liu, X Zhao, More general averaging formulae for preimage classes, Topology Appl. 267 (2019) 106875 MR4002162
17 W S Massey, Algebraic topology: an introduction, 56, Springer (1977) MR448331
18 J Mawhin, M Willem, Critical point theory and Hamiltonian systems, 74, Springer (1989) MR982267
19 G D de Melo, D Vendrúscolo, Nielsen–Borsuk–Ulam number for maps between tori, J. Fixed Point Theory Appl. 25 (2023) 61 MR4597667
20 H A dos Santos, P Wong, Equivariant Nielsen root theory for G-maps, Topology Appl. 157 (2010) 1839 MR2639848
21 K Tsai-han, The theory of fixed point classes, Springer (1989) MR1002187
22 P Wong, Equivariant Nielsen numbers, Pacific J. Math. 159 (1993) 153 MR1211390
23 C T Yang, On theorems of Borsuk–Ulam, Kakutani–Yamabe–Yujobô and Dyson, I, Ann. of Math. 60 (1954) 262 MR65910