Fixed point theory and trace for bicategories
Astérisque, no. 333 (2010) , 114 p.
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     publisher = {Soci\'et\'e math\'ematique de France},
     number = {333},
     year = {2010},
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     zbl = {1207.18001},
     language = {en},
     url = {http://www.numdam.org/item/AST_2010__333__R1_0/}
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Ponto, Kate. Fixed point theory and trace for bicategories. Astérisque, no. 333 (2010), 114 p. http://numdam.org/item/AST_2010__333__R1_0/

[1] M. A. Armstrong - Basic topology, Undergraduate Texts in Mathematics, Springer, 1983, Corrected reprint of the 1979 original. | MR | Zbl | DOI

[2] R. F. Brown - The Lefschetz fixed point theorem, Scott, Foresman and Co., Glenview, Ill.-London, 1971. | MR | Zbl

[3] M. G. Citterio - "The Reidemeister number as a homotopy equalizer", Rend. Mat. Appl. 18 (1998), p. 87-101. | MR | Zbl

[4] V. Coufal - "A family version of Lefschetz-Nielsen fixed point theory", Ph.D. Thesis, University of Notre Dame, 2004. | MR

[5] V. Coufal, "A base-point-free definition of the Lefschetz invariant", Fixed Point Theory Appl. Special Issue (2006), Art. ID 34143, 20. | MR | Zbl | EuDML

[6] M. Crabb & I. James - Fibrewise homotopy theory, Springer Monographs in Math., Springer London Ltd., 1998. | MR | Zbl

[7] A. Dold - "Fixed point index and fixed point theorem for Euclidean neighborhood retracts", Topology 4 (1965), p. 1-8. | MR | Zbl | DOI

[8] A. Dold, "The fixed point index of fibre-preserving maps", Invent. Math. 25 (1974), p. 281-297. | MR | Zbl | EuDML | DOI

[9] A. Dold, "The fixed point transfer of fibre-preserving maps", Math. Z. 148 (1976), p. 215-244. | MR | Zbl | EuDML | DOI

[10] A. Dold, Lectures on algebraic topology, Classics in Mathematics, Springer, 1995, Reprint of the 1972 edition. | MR | Zbl | DOI

[11] A. Dold & D. Puppe - "Duality, trace, and transfer", in Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), PWN, 1980, p. 81-102. | MR | Zbl

[12] E. R. Fadell & S. Husseini - "A fixed point theory for fiber-preserving maps", in Fixed point theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, 1981, p. 49-72. | MR | Zbl | DOI

[13] S. Gen-Hua - "On least number of fixed points and Nielsen numbers", Chinese Math.-Acta 8 (1966), p. 234-243. | MR

[14] R. Geoghegan - "Nielsen fixed point theory", in Handbook of geometric topology, North-Holland, 2002, p. 499-521. | MR | Zbl

[15] I. M. Hall - "The generalized Whitney sum", Quart. J. Math. Oxford Ser. 16 (1965), p. 360-384. | MR | Zbl | DOI

[16] A. Hatcher - Algebraic topology, Cambridge Univ. Press, 2002. | MR | Zbl

[17] P. R. Heath - "Product formulae for Nielsen numbers of fibre maps", Pacific J. Math. 117 (1985), p. 267-289. | MR | Zbl | DOI

[18] P. R. Heath, E. Keppelmann & P. Wong - "Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps", Topology Appl. 67 (1995), p. 133-157. | MR | Zbl | DOI

[19] S. Husseini - "Generalized Lefschetz numbers", Trans. Amer. Math. Soc. 272 (1982), p. 247-274. | MR | Zbl | DOI

[20] J. Jezierski & W. Marzantowicz - Homotopy methods in topological fixed and periodic points theory, Topological Fixed Point Theory and Its Applications, vol 3, Springer, 2006. | MR | Zbl

[21] B. J. Jiang - Lectures on Nielsen fixed point theory, Contemporary Mathematics, vol. 14, Amer. Math. Soc, 1983. | MR | Zbl | DOI

[22] B. J. Jiang, "Fixed points and braids. II", Math. Ann. 272 (1985), p. 249-256. | MR | Zbl | EuDML | DOI

[23] A. Joyal, R. Street & D. Verity - "Traced monoidal categories", Math. Proc. Cambridge Philos. Soc. 119 (1996), p. 447-468. | MR | Zbl | DOI

[24] G. M. Kelly - Basic concepts of enriched category theory, London Mathematical Society Lecture Note Series, vol. 64, Cambridge Univ. Press, 1982. | MR | Zbl

[25] J. R. Klein & E. B. Williams - "Homotopical intersection theory. I", Geom. Topol. 11 (2007), p. 939-977. | MR | Zbl | DOI

[26] C. Lee - "A minimum fixed point theorem for smooth fiber preserving maps", Proc. Amer. Math. Soc. 135 (2007), p. 1547-1549. | MR | Zbl | DOI

[27] T. Leinster - "Basic bicategories", preprint arXiv:math/9810017.

[28] L. G. J. Lewis, J. P. May, M. Steinberger & J. E. Mcclure - Equivariant stable homotopy theory, Lecture Notes in Math., vol. 1213, Springer, 1986. | MR | Zbl

[29] S. Mac Lane - Categories for the working mathematician, second ed., Graduate Texts in Math., vol. 5, Springer, 1998. | MR | Zbl

[30] G. Maltsiniotis - "Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées", Cahiers Topologie Géom. Différentielle Catég. 36 (1995), p. 195-288. | MR | Zbl | EuDML | Numdam

[31] J. P. May - "Classifying spaces and fibrations", Mem. Amer. Math. Soc. 1 (1975). | MR | Zbl

[32] J. P. May, "The additivity of traces in triangulated categories", Adv. Math. 163 (2001), p. 34-73. | MR | Zbl | DOI

[33] J. P. May, "Picard groups, Grothendieck rings, and Burnside rings of categories", Adv. Math. 163 (2001), p. 1-16. | MR | Zbl | DOI

[34] J. P. May & J. Sigurdsson - Parametrized homotopy theory, Mathematical Surveys and Monographs, vol. 132, Amer. Math. Soc, 2006. | MR | Zbl | DOI

[35] A. Nicas - "Trace and duality in symmetric monoidal categories", K -Theory 35 (2005), p. 273-339. | MR | Zbl | DOI

[36] B. Norton-Odenthal - "A product formula for the generalized Lefschetz number", Ph.D. Thesis, University of Wisconsin, Madison, 1991.

[37] B. Pareigis - Non-additive ring and module theory. V. Projective and coflat objects, München : Verlag Uni-Druck, 1980. | Zbl

[38] K. Ponto & M. Shulman - "Shadows and traces in bicategories", preprint arXiv:0910.1306. | MR | Zbl | DOI

[39] A. Ranicki - "The algebraic theory of surgery. II. Applications to topology", Proc. London Math. Soc. 40 (1980), p. 193-283. | MR | Zbl | DOI

[40] K. Reidemeister - "Automorphismen von Homotopiekettenringen", Math. Ann. 112 (1936), p. 586-593. | MR | JFM | EuDML | DOI

[41] J. L. Scofield - "Nielsen fixed point theory for fiber-preserving maps", Ph.D. Thesis, University of Wisconsin, Madison, 1985. | MR

[42] M. Shulman - "Homotopy limits and colimits and enriched homotopy theory", preprint arXiv:math/0610194.

[43] J. Stallings - "Centerless groups-an algebraic formulation of Gottlieb's theorem", Topology 4 (1965), p. 129-134. | MR | Zbl | DOI

[44] A. Strøm - "The homotopy category is a homotopy category", Arch. Math. (Basel) 23 (1972), p. 435-441. | MR | Zbl | DOI

[45] F. Wecken - "Fixpunktklassen. II. Homotopieinvarianten der Fixpunkttheorie", Math. Ann. 118 (1941), p. 216-234. | MR | JFM | EuDML

[46] F. Wecken, "Fixpunktklassen. III. Mindestzahlen von Fixpunkten", Math. Ann. 118 (1942), p. 544-577. | MR | JFM | EuDML