An appreciation of the work of Samuel Eilenberg (1913-1998)

• Autorzy: May J. P.
• Konferencja: 6th European Congress of Mathematics, 2-7 July 2012 Kraków
• Języki publikacji: EN

Słowa kluczowe

EN

Eilenberg Samuel; mathematical work; scientific biography

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2012
• Tom: T. 48, Nr 2
• Strony: 185--197
• Opis fizyczny: Bibliogr. 63 poz.

Twórcy

autor

May J. P.

• Department of Mathematics, University of Chicago, 5734 South University Avenue Chicago, IL 60637,USA

Bibliografia

• [1] H. Bass, H. Cartan, P. Freyd, A. Heller, S. Mac Lane, Samuel Eilenberg (1913-1918), Notices AMS 45 (1998), 1344-1351, reprinted in Biographical Memoirs, vol. 79, National Academy of Sciences in Washington, Washington DC 2001, 106-133.
• [2] H. Brownrigg, Betel cutters: from the Samuel Eilenberg collection, Thames and Hudson 1992.
• [3] H. Cartan, S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton 1956.
• [4] H. Cartan, Mathematical Review. MR0050886 (14 398b).
• [5] H. Cartan et al., Seminaire H. Cartan de I’ENS, 1954-55. Algebres d’Eilenberg-MacLane et homotopie. Secr, math., 11, R.P. Curie (1956).
• [6] C. Chevalley, S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85-124.
• [7] G. Eilenberg, Sur le prolongement des transformations en surfaces sphériques, Fund. Math. 31 (1938), 179-200.
• [8] S. Eilenberg, Cohomology and continuous mappings, Annals of Mathematics 41 (1940), 231-251.
• [9] S. Eilenberg, On continuous mappings of manifolds into spheres, Annals of Mathematics 41 (1940), 662-673.
• [10] S. Eilenberg, Singular homology theory, Ann. of Math. 45 (1944), 407-447.
• [11] S. Eilenberg, Homology of spaces with operators. I, Trans. Amer. Math. Soc. 61 (1947). 378-417- Errata, 62, 548 (1947).
• [12] S. Eilenberg, Automata, languages, and machines, A, Pure and Applied Mathematics, vol. 58, Academic Press (A subsidiary of Harcourt Brace Jovanovich, Publishers), New York 1974.
• [13] S. Eilenberg, Automata, languages, and machines, B, Pure and Applied Mathematics, vol. 59, Academic Press (A subsidiary of Harcourt Brace Jovanovich, Publishers), New York-London 1976. With two chapters ("Depth decomposition theorem" and "Complexity of semigroups and morphisms") by Bret Tilson.
• [14] S. Eilenberg, G. M. Kelly, Closed categories, 1966 Proc. Conf. Categorical Algebra (Lajolla, Calif., 1965), 421-562.
• [15] S. Eilenberg, K. Kuratowski, A remark on duality, Fund. Math. 50 (1961/1962), 515-517.
• [16] S. Eilenberg, S. Mac Lane, Infinite cycles and homologies, Proc. Acad. Sci. U.S.A. 27 (1941), 535-539.
• [17] S. Eilenberg, S. Mac Lane, Group extensions and homology, Ann. of Math. 43 (1942), 757-831.
• [18] S. Eilenberg, S. Mac Lane, Natural isomorphisms in group theory, Proc. Nat. Acad. Sci. USA 28 (1942), 537-543.
• [19] S. Eilenberg, S. MacLanc, Relations betwen hnmnlngy and homulupy groups, Proc. Nat. Acad. Sci. U. S. A. 29 (1943), 155-158.
• [20] S. Eilenberg, S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294.
• [21] S. Eilenberg, S. Mac Lane, Relations between homology and homotopy groups of spaces, Annals of Math. 46 (1945), 480-509.
• [22] S. Eilenberg, S. Mac Lane, Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 277-280.
• [23] S. Eilenberg, S. Mac Lane, Cohomology theory in abstract groups. I, Ann. of Math. 48 (1947), 51-78.
• [24] S. Eilenberg, S. Mac Lane, Cohomology theory in abstract groups. II. Group extensions with a non-Abelian kernel, Ann. of Math. 48 (1947), 326-341.
• [25] S. Eilenberg, S. Mac Lane, Algebraic cohomology groups and loops, Duke Math. J. 14 (1947), 435-463.
• [26] S. Eilenberg, S. Mac Lane, Cohomology and Galois theory. I. Normality of algebras and Teichmuller’s cocycle, Trans. Amer. Math. Soc. 64 (1948), 1-20.
• [27] S. Eilenberg, S. Mac Lane, Homology of spaces with operators. II, Trans. Amer. Math. Soc. 65 (1949), 49-99.
• [28] S. Eilenberg, S. Mac Lane, Relations between homology and homotopy groups of spaces. 11, Ann. of Math. 51 (1950), 514-533.
• [29] S. Eilenberg, S. Mac Lane, Cohomology theory of Abelian groups and homotopy theory. I, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 443-447.
• [30] S. Eilenberg, S. Mac Lane, Cohomology theory of Abelian groups and homotopy theory. II, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 657-663.
• [31] S. Eilenberg, S. Mac Lane, Cohomology theory of Abelian groups and homotopy theory. III, Proc. Nat. Acad. Sci. U.S.A. 37 (195l), 307-310.
• [32] S. Eilenberg, S. Mac Lane, Acyclic models, Amer. J. Math. 75 (1953), 189- 199
• [33] S. Eilenberg, S. Mac Lane, On the groups H(Π,n). I, Ann. of Math. 58 (1953), 55-106.
• [34] S. Eilenberg, S. Mac Lane, On the groups H(Π,n). II. Methods of computation, Ann. of Math. 60 (1954), 49-139.
• [35] S. Eilenberg, S. Mac Lane, On the groups H (Π, n). III, Ann. of Math. 60 (1954), 513-557.
• [36] S. Eilenberg, S. Mac Lane, Eilenberg-MacLane collected works, Academic Press, Orlando 1986.
• [37] S. Eilenberg, D. Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214-222.
• [38] S. Eilenberg, J. C. Moore, Limits and spectral sequences, Topology 1 (1962), 1-23.
• [39] S. Eilenberg, J.C. Moore, Homological algebra and fibrations, Colloque de Topologie (Brussels, 1964), 81-90. Librairie Universitaire, Louvain.
• [40] S. Eilenberg, J. C. Moore, Foundations of relative homological algebra, Mem. Amer. Math. Soc. 55 (1965).
• [41] S. Eilenberg, J. C. Moore, Adjoint functors and triples, Illinois J Math. 9 (1965), 381-398.
• [42] S. Eilenberg, J. C.Moore, Homology and fibrations. I. Coalgebras, cotensor product and its derived functors, Comment. Math. Helv. 40 (1966), 199-236.
• [43] S. Eilenberg, T. Nakayama, On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings, Nagoya Math. J. 9 (1955), 1-16.
• [44] S. Eilenberg, 1. Niven, The "fundamental theorem of algebra" for quaternions, Bull. Amer. Math. Soc. 50 (1944), 246-248.
• [45] S. Eilenberg, N.E. Steenrod, Axiomatic approach to homology theory, Proc. Nat. Acad. of Sci. U.S.A. 31 (1945), 117-120.
• [46] S. Eilenberg, N.E. Steenrod, The foundations of algebraic topology, Princeton University Press, Princeton 1952.
• [47] S. Eilenberg, J. A. Zilber, Semi-simplicial complexes and singular homology, Ann. of Math. 51 (1950), 499-5!3.
• [48] S. Eilenberg, J.A. Zilber, On products of complexes, Amer. J. Math. 75 (1953), 200-204.
• [49] V. K. A. M. Gugenheim, J. P. May, On the theory and applications of differential torsion products, Memoirs Amer. Math. Soc. 142 (1974).
• [50] A. Heller, M. Tierney, Algebra, topology, and category theory, Academic Press 1976.
• [51] S. Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, vol. 27, American Mathematical Society, New York 1942.
• [52] M. Lerner, S. M. Kossak, The lotus transcendent: Indian and Southeast Asian sculpture from the Samuel Eilenberg Collection, Metropolitan Museum of Art Series 1991.
• [53] S. Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28-46.
• [54] S. Mac Lane, The work of Samuel Eilenberg in topology. Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), Academic Press, New York 1976, 133-144.
• [55] S. Mac Lane, Samuel Eilenberg and topology, (in Polish), Wiad. Mat. 25 (1984), 229-242. Translated from English by Roman Duda.
• [56] S. Mac Lane, Categories for the working mathematician, 2nd ed., Springer 1998.
• [57] J.P. May, Stable algebraic topology, in: History of topology (I. M. James, ed.), Elsevier Science B.V., Amsterdam 1999.
• [58] J.P. May, The additivity of traces in triangulated categories, Advances in Mathematics 163 (2001), 34-73.
• [59] J.P. May, Memorial talk [for Saunders Mac Lane], J. Homotopy Relat. Struct. 2 (2007), 11-12.
• [60] J. Milnor, Construction of universal bundles, II, Ann. of Math. 63 (1956), 272-280.
• [61] M. Rothenberg, N. E. Steenrod, The cohomology of classifying spaces of H-spaces, Bull. Amer. Math. Soc. 71 (1965), 872-875.
• [62] J.-P. Serre, Cohomologie modulo 2 des complexes d’Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198-232.
• [63] D. Simovici, Mathematical Review: MR0530382 (58 26604a) and MR0530383 (5826604b).