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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction................................ 5
1. Preliminaries.......................... 5
2. When is the symmetric product a manifold?.............. 12
3. When is the cyclic product a manifold?............................................................................................. 17
4. When is the permutation product a manifold? The characterization problem........................... 22
5. Permutation products of the punctured cell and two-dimensional half-space.......................... 28
6. Permutation products of the annulus................................................................................................ 34
7. The second permutation product of the torus.................................................................................. 41
8. Summary of known characterizations................................................................................................ 46
References and bibliography.................................................................................................................. 47
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
182
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXII
Daty
wydano
1980
Twórcy
autor
Bibliografia
- [1] H. Bass, A. Heller, and R. Swan, The Whitehead group of a polynomial extension. Publ. I.H.E.S., No. 22 (1964), pp. 61-79.
- [2] K. Borsuk and S. Ulam, On symmetric products of topological spaces. Bull. Amer. Math. Soc. 37 (1931), pp. 875-882.
- [3] K. Borsuk, On the third symmetric potency of the circumference, Fund. Math. 36 (1949), pp. 235-244.
- [4] R. Bott, On the third symmetric potency of $S_1$, ibid. 39 (1952), pp. 264-268.
- [5] M. Brown, Locally flat inbeddings of topological manifolds, Ann. of Math. 75 (1962), pp. 331-341.
- [6] A. Dold, Homology of symmetric products and other functors of complexes, ibid. 68 (1958), pp. 54-80.
- [7] J. Dugundji, Topology, Allyn and Bacon, 1966.
- [8] T. Ganea, Symmetrische Potenzen topologischer Raume, Math. Nach. 11 (1954), pp. 305-316.
- [9] M. Greenberg, Lectures on algebraic topology, Benjamin, 1967.
- [10] G. Higman, The units of group rings, Proc. London Math. Soc. 46 (1940), pp. 231-248.
- [11] J. F. P. Hudson, Piecewise linear topology, Benjamin, 1969.
- [12] W. Hurewicz and H. Wallman, Dimension theory, Princeton Mathematical Series No. 4, Princeton University Press, 1941.
- [13] I. M. James, E. Thomas, H. Toda, and G. W. Whitehead, On the symmetric square of a sphere, J. Math, and Mech. 12 (1963), pp. 771-776.
- [14] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), pp. 742-749.
- [15] R. C. Kirby and L. C. Siebenmann, Foundations of topology, Notices Amer. Math. Soc. 16 (1969), p, 848.
- [16] L. V. Keldys, Topological imbeddings in Euclidean space, Proceedings of the Steklov Institute of Mathematics No. 81, Amer. Math. Soc., 1968.
- [17] K. Kwun, Uniqueness of the open cone neighborhood, Proc. Amer. Math. Soc. 15 (1964), pp. 476-479.
- [18] R. C. Lacher, Cell-like spaces, ibid. 20 (1969), pp. 598-602.
- [19] S. D. Liao, On the topology of cyclic products of spheres, Trans. Amer. Math. Soc. 77 (1954), pp. 520-551.
- [20] C. Lovetro, Jr., Symmetric and permutation product spaces, M. S. Thesis, Louisiana State University, 1966.
- [21] I. G. Macdonald, The Poincare polynomial of a symmetric product, Proc. Camb. Phil. Soc. 58 (1962), pp. 563-568.
- [22] D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. 79 (1964), pp. 327-337.
- [23] E. A. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), pp. 152-182.
- [24] J. Milnor, h-cobordism, Princeton Mathematical Notes, Princeton University Press, 1965.
- [25] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), pp. 358-426.
- [26] R. Molski, On symmetric product. Fund. Math. 44 (1957), pp. 165-170.
- [27] H. R. Morton, Symmetric products of the circle, Proc. Camb. Phil. Soc. 63 (1967), pp. 349-352.
- [28] J. Nagata. Modern dimension theory, Interscience, 1965.
- [29] M. Richardson. On the homology characters of symmetric products, Duke Math. J. 1 (1935), pp. 50-59.
- [30] R. M. Schori, Hyperspaces and symmetric products of topological spaces. Fund. Math. 63 (1968), pp. 77 88.
- [31] R. Schori and J. E. West, $2^1$ is homeomorphic to the Hilbert cube. Bull. Amer. Math. Soc. 78 (1972), pp. 402-406.
- [32] P. A. Smith. The topology of involutions. Proc. Nat. Acad. Sci. 19 (1933), pp. 612-618.
- [33] E. Spanier. Algebraic topology, McGraw-Hill. 1966.
- [34] L. Steen and J. Seebach, Jr., Counterexamples in topology. Holt, Rinehart and Winston. 1970.
- [35] N. Steenrod. Reviews of papers in algebraic and differential topology, topological groups, and homological algebra, Amer. Math. Soc. 1968.
- [36] S. K. Stein. Homology of the two-fold symmetric product, Ann. of Math. (2) 59 (1954), pp. 570 583.
- [37] R. Swan. The homology of cyclic products. Trans. Amer. Math. Soc. 95 (1960), pp. 27-68.
- [38] R.J. Walker. The Betti numbers of cyclic products. Bull Amer. Math. Soc. 42 (1936), pp. 709 714.
- [39] J. H. C. Whitehead. Simple homotopy types. Amer. J. Math. 72 (1940), pp. 1-57.
- [40] W. Wu, Note sur les produits essentiels symétriques des espaces topologique, I Comptes Rendus des Séances de l'Academie des Sciences 16 (1947), pp. 1139-1141.
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