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References
M. Arkowitz, and R. F. Brown, The Lefschetz-Hopf theorem and axioms for the Lefschetz number, Preprint.
H.-J. Baues and D. L. Ferrario, Homotopy and homology of fibred spaces, Topology Appl. (2003) (to appear).
J. Better, Relative equivariant Nielsen fixed point theory, Ph.D. Thesis (2002), UCLA..
G. E. Bredon, Equivariant Cohomology Theories, Springer—Verlag, Berlin, 1967.
R. F. Brown, On the Lefschetz number and the Euler class, Trans. Amer. Math. Soc. 118 (1965), 174–179.
_____, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.—London, 1971.
A. Dold, Fixed point index and fixed point theorem for Euclidean neighbourhood retracts, Topology 4 (1965), 1–8.
_____, K-theory of non-additive functors of finite degree, Math. Ann. 196 (1972), 177–197.
_____, The fixed point index of fibre-preserving maps, Invent. Math. 25 (1974), 281–297.
_____, Fixed point indices of iterated maps., Invent. Math. 74 (1983), 419–435.
E. Fadell and P. Wong, On deforming G-maps to be fixed point free, Pacific J. Math. 132 (1988), 277–281.
P. L. Fagundes, Equivariant Nielsen coincidence theory, Mat. Contemp. 13 (1997), 117–142, 10th Brazilian Topology Meeting (Sao Carlos, 1996).
P. L. Fagundes and D. L. Gonçalves, Fixed point indices of equivariant maps of certain Jiang spaces, Topol. Methods Nonlinear Anal. 14 (1999), 151–158.
J. S. Fares and E. L. Hart, A generalized Lefschetz number for local Nielsen fixed point theory, Topology Appl. 59 (1994), 1–23.
D. L. Ferrario, A fixed point index for equivariant maps, Topol. Methods Nonlinear Anal. 13 (1999), 313–340.
_____, Generalized Lefschetz numbers of pushout maps defined on non-connected spaces, Nielsen Theory and Reidemeister Torsion (Warsaw 1996), Polish Acad. Sci., Warsaw, 1999, pp. 117–135.
_____, Equivariant deformations of manifolds and real representations, Pacific J. Math. 196 (2000), 353–368.
_____, A Möbius inversion formula for generalized Lefschetz numbers, Osaka J. of Math. 4 (2003), 1–27.
_____, On the equivariant Hopf theorem, Topology 42 (2003), 447–465.
T. N. Fomenko, On the least number of fixed points of an equivariant mapping, Mat. Zametki 69 (2001), 100–112.
R. Geoghegan and A. Nicas, Trace and torsion in the theory of flows, Topology 33 (1994), 683–719.
J. Guo and P. R. Heath, Equivariant coincidence Nielsen numbers, Topology Appl. 128 (2003), 277–308.
H. Honkasalo and E. Laitinen, Equivariant Lefschetz classes in Alexander-Spanier cohomology, Osaka J. Math. 33 (1996), 793–804.
M. Izydorek and A. Vidal, A note on the converse of the Lefschetz theorem for G-maps, Ann. Polon. Math. 58 (1993), 177–183.
_____, An example concerning equivariant deformations, Topol. Methods Nonlinear Anal. 15 (2000), 187–190, Dedicated to Juliusz Schauder, 1899–1943.
J. Jezierski, A modification of the relative Nielsen number of H. Schirmer, Topology Appl. 62 (1995), 45–63.
K. Komiya, A necessary and sufficient condition for the existence of non-singularG-vector fields on G-manifolds, Osaka J. Math. 13 (1976), 537–546.
_____, G-manifolds and G-vector fields with isolated zeros, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), 124–127.
_____, The Lefschetz number for equivariant maps, Osaka J. Math. 24 (1987), 299–305.
_____, Fixed point indices of equivariant maps and Möbius inversion, Invent. Math. 91 (1988), 129–135.
E. Laitinen, On the Burnside ring and stable cohomotopy of a finite group, Math. Scand. 44 (1979), 37–72.
_____, Unstable homotopy theory of homotopy representations, Transformation Groups (Poznań, 1985), Lecture Notes in Math., vol. 1217, Springer, Berlin, 1986, pp. 210–248.
E. Laitinen and W. Lück, Equivariant Lefschetz classes, Osaka J. Math. 26 (1989), 491–525.
W. Lück, The universal functorial Lefschetz invariant, Algebraic Topology (Kazimierz Dolny, 1997), Fund. Math. 161 (1999), 167–215.
W. Marzantowicz, A formula for the G-Euler characteristic, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), 565–570.
_____, The Lefschetz number in equivariant K-theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 901–906.
W. Marzantowicz and C. Prieto, Generalized Lefschetz numbers for equivariant maps, Osaka J. Math. 39 (2002), 821–841.
_____, A decomposition of equivariant stable homotopy classes and a computation of the first equivariant stem, Preprint.
_____, The unstable equivariant fixed point index and the equivariant degree., J. London Math. Soc. (2003) (to appear).
B. Norton-Odenthal and P. Wong, A relative generalized Lefschetz number, Topology Appl. 56 (1994), 141–157.
C. Prieto and H. Ulrich, Equivariant fixed point index and fixed point transfer in nonzero dimensions, Trans. Amer. Math. Soc. 328 (1991), 731–745.
H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459–473.
H. Steinlein, Ein Satz über den Leray-Schauderschen Abbildungsgrad, Math. Z. 126 (1972), 176–208.
T. tom Dieck, Transformation Groups, Walter de Gruyter & Co., Berlin, 1987.
H. Ulrich, Fixed point theory of parametrized equivariant maps, Lecture Notes in Math., vol. 1343, Springer—Verlag, Berlin, 1988.
A. Vidal, On equivariant deformation of maps, Publ. Mat. 32 (1988), 115–121.
D. Wilczyński, Fixed point free equivariant homotopy classes, Fund. Math. 123 (1984), 47–60.
P. Wong, Equivariant Nielsen fixed point theory for G-maps, Pacific J. Math. 150 (1991), 179–200.
_____, Equivariant path fields on G-complexes, Rocky Mountain J. Math. 22 (1992), 1139–1145.
_____, Equivariant Nielsen fixed point theory and periodic points, Nielsen Theory and Dynamical Systems (South Hadley, MA, 1992), Contemp. Math. 152 (1993), 341–350.
_____, Equivariant Nielsen numbers, Pacific J. Math. 159 (1993), 153–175.
_____, Equivariant Nielsen theory, Nielsen Theory and Reidemeister Torsion (Warsaw, 1996), Banach Center Publ. 49 (1999), Polish Acad. Sci., Warsaw, 253–258.
, Nielsen fixed point theory for partially ordered sets, Topology Appl. 110 (2001), 185–209.
P. P. ZabreÄiko and M. A. Krasnosel'skiÄ, Iterations of operators, and fixed points, Dokl. Akad. Nauk SSSR 196 (1971), 1006–1009.
X. Zhao, On minimal fixed point numbers of relative maps, Topology Appl. 112 (2001), 41–70.
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Ferrario, D.L. (2005). A Note on Equivariant Fixed Point Theory. In: Brown, R.F., Furi, M., Górniewicz, L., Jiang, B. (eds) Handbook of Topological Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3222-6_8
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