@book{AST_2010__333__R1_0, author = {Ponto, Kate}, title = {Fixed point theory and trace for bicategories}, series = {Ast\'erisque}, publisher = {Soci\'et\'e math\'ematique de France}, number = {333}, year = {2010}, mrnumber = {2741967}, zbl = {1207.18001}, language = {en}, url = {http://www.numdam.org/item/AST_2010__333__R1_0/} }
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] Basic topology, Undergraduate Texts in Mathematics, Springer, 1983, Corrected reprint of the 1979 original. | MR | Zbl | DOI
-[2] The Lefschetz fixed point theorem, Scott, Foresman and Co., Glenview, Ill.-London, 1971. | MR | Zbl
-[3] The Reidemeister number as a homotopy equalizer", Rend. Mat. Appl. 18 (1998), p. 87-101. | MR | Zbl
- "[4] A family version of Lefschetz-Nielsen fixed point theory", Ph.D. Thesis, University of Notre Dame, 2004. | MR
- "[5] A base-point-free definition of the Lefschetz invariant", Fixed Point Theory Appl. Special Issue (2006), Art. ID 34143, 20. | MR | Zbl | EuDML
, "[6] Fibrewise homotopy theory, Springer Monographs in Math., Springer London Ltd., 1998. | MR | Zbl
& -[7] Fixed point index and fixed point theorem for Euclidean neighborhood retracts", Topology 4 (1965), p. 1-8. | MR | Zbl | DOI
- "[8] The fixed point index of fibre-preserving maps", Invent. Math. 25 (1974), p. 281-297. | MR | Zbl | EuDML | DOI
, "[9] The fixed point transfer of fibre-preserving maps", Math. Z. 148 (1976), p. 215-244. | MR | Zbl | EuDML | DOI
, "[10] Lectures on algebraic topology, Classics in Mathematics, Springer, 1995, Reprint of the 1972 edition. | MR | Zbl | DOI
,[11] Duality, trace, and transfer", in Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), PWN, 1980, p. 81-102. | MR | Zbl
& - "[12] 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] On least number of fixed points and Nielsen numbers", Chinese Math.-Acta 8 (1966), p. 234-243. | MR
- "[14] Nielsen fixed point theory", in Handbook of geometric topology, North-Holland, 2002, p. 499-521. | MR | Zbl
- "[15] The generalized Whitney sum", Quart. J. Math. Oxford Ser. 16 (1965), p. 360-384. | MR | Zbl | DOI
- "[16] Algebraic topology, Cambridge Univ. Press, 2002. | MR | Zbl
-[17] Product formulae for Nielsen numbers of fibre maps", Pacific J. Math. 117 (1985), p. 267-289. | MR | Zbl | DOI
- "[18] 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] Generalized Lefschetz numbers", Trans. Amer. Math. Soc. 272 (1982), p. 247-274. | MR | Zbl | DOI
- "[20] Homotopy methods in topological fixed and periodic points theory, Topological Fixed Point Theory and Its Applications, vol 3, Springer, 2006. | MR | Zbl
& -[21] Lectures on Nielsen fixed point theory, Contemporary Mathematics, vol. 14, Amer. Math. Soc, 1983. | MR | Zbl | DOI
-[22] Fixed points and braids. II", Math. Ann. 272 (1985), p. 249-256. | MR | Zbl | EuDML | DOI
, "[23] Traced monoidal categories", Math. Proc. Cambridge Philos. Soc. 119 (1996), p. 447-468. | MR | Zbl | DOI
, & - "[24] Basic concepts of enriched category theory, London Mathematical Society Lecture Note Series, vol. 64, Cambridge Univ. Press, 1982. | MR | Zbl
-[25] Homotopical intersection theory. I", Geom. Topol. 11 (2007), p. 939-977. | MR | Zbl | DOI
& - "[26] A minimum fixed point theorem for smooth fiber preserving maps", Proc. Amer. Math. Soc. 135 (2007), p. 1547-1549. | MR | Zbl | DOI
- "[27] Basic bicategories", preprint arXiv:math/9810017.
- "[28] Equivariant stable homotopy theory, Lecture Notes in Math., vol. 1213, Springer, 1986. | MR | Zbl
, , & -[29] Categories for the working mathematician, second ed., Graduate Texts in Math., vol. 5, Springer, 1998. | MR | Zbl
-[30] 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] Classifying spaces and fibrations", Mem. Amer. Math. Soc. 1 (1975). | MR | Zbl
- "[32] The additivity of traces in triangulated categories", Adv. Math. 163 (2001), p. 34-73. | MR | Zbl | DOI
, "[33] Picard groups, Grothendieck rings, and Burnside rings of categories", Adv. Math. 163 (2001), p. 1-16. | MR | Zbl | DOI
, "[34] Parametrized homotopy theory, Mathematical Surveys and Monographs, vol. 132, Amer. Math. Soc, 2006. | MR | Zbl | DOI
& -[35] Trace and duality in symmetric monoidal categories", -Theory 35 (2005), p. 273-339. | MR | Zbl | DOI
- "[36] A product formula for the generalized Lefschetz number", Ph.D. Thesis, University of Wisconsin, Madison, 1991.
- "[37] Non-additive ring and module theory. V. Projective and coflat objects, München : Verlag Uni-Druck, 1980. | Zbl
-[38] Shadows and traces in bicategories", preprint arXiv:0910.1306. | MR | Zbl | DOI
& - "[39] The algebraic theory of surgery. II. Applications to topology", Proc. London Math. Soc. 40 (1980), p. 193-283. | MR | Zbl | DOI
- "[40] Automorphismen von Homotopiekettenringen", Math. Ann. 112 (1936), p. 586-593. | MR | JFM | EuDML | DOI
- "[41] Nielsen fixed point theory for fiber-preserving maps", Ph.D. Thesis, University of Wisconsin, Madison, 1985. | MR
- "[42] Homotopy limits and colimits and enriched homotopy theory", preprint arXiv:math/0610194.
- "[43] Centerless groups-an algebraic formulation of Gottlieb's theorem", Topology 4 (1965), p. 129-134. | MR | Zbl | DOI
- "[44] The homotopy category is a homotopy category", Arch. Math. (Basel) 23 (1972), p. 435-441. | MR | Zbl | DOI
- "[45] Fixpunktklassen. II. Homotopieinvarianten der Fixpunkttheorie", Math. Ann. 118 (1941), p. 216-234. | MR | JFM | EuDML
- "[46] Fixpunktklassen. III. Mindestzahlen von Fixpunkten", Math. Ann. 118 (1942), p. 544-577. | MR | JFM | EuDML
, "