On the work of L. V. Keldysh and her seminar

A. V. Chernavskii

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 4, pp. 589-614

Résumé

A survey of the work of Professor Lyudmila Vsevolodovna Keldysh in the areas of descriptive set theory and topology is presented together with a survey of the work of members of the geometric topology seminar she led from 1959 to 1973 at the Steklov Institute of Mathematics.

Bibliographie

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[15] L. Keldysh, “Nepreryvnye otobrazheniya segmenta na $n$-mernyi kub”, Dokl. AN SSSR, 66:3 (1949), 327–330 | MR | Zbl

[16] L. Keldysh, “Nulmernye otobrazheniya, povyshayuschie razmernost”, Matem. sb., 28:3 (1951), 537–566 | MR | Zbl

[17] L. Keldysh, “Nulmernye otkrytye otobrazheniya”, Izv. AN SSSR. Ser. matem., 23:2 (1959), 165–184 | MR | Zbl

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[28] D. Wilson, “Open mappings on manifolds and a counterexample to the Whyburn conjecture”, Duke Math. J., 40:3 (1973), 705–716 | DOI | MR | Zbl

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[32] Yu. Yu. Trokhimchuk, “O nepreryvnykh otobrazheniyakh oblastei evklidova prostranstva”, Ukr. matem. zhurn., 16:2 (1964), 196–211 | MR | Zbl

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[35] A. V. Chernavskii, “Dopolnenie k state «O konechnokratnykh otkrytykh otobrazheniyakh»”, Matem. sb., 66:3 (1965), 471–472 | MR

[36] A. M. Rodnyanskii, “O nepreryvnykh i differentsiruemykh otobrazheniyakh otkrytykh mnozhestv evklidova prostranstva”, Matem. sb., 42:2 (1957), 179–196 | MR

[37] L. Keldysh, “Primer monotonnogo neprivodimogo otobrazheniya trekhmernogo kuba na chetyrekhmernyi”, Dokl. AN SSSR, 103:6 (1955), 957–960 | MR | Zbl

[38] L. Keldysh, “Preobrazovanie monotonnogo neprivodimogo otobrazheniya v monotonno-okrytoe i monotonno-okrytye otobrazheniya kuba, povyshayuschie razmernost”, Matem. sb., 43:2 (1957), 187–226 | MR | Zbl

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[41] V. P. Kompaniets, “O monotonnykh otobrazheniyakh $n$-mernoi sfery na sebya”, Ukr. matem. zhurn., 17:6 (1965), 100–103 | MR | Zbl

[42] A. V. Chernavskii, “Obobschenie postroeniya L. V. Keldysh monotonnogo otobrazheniya kuba na kub bolshei razmernosti”, UMN, 40:4 (1985), 209–211 | MR

[43] S. P. Novikov, “O letnem topologicheskom institute (Siettl, 1963, SShA)”, UMN, 20:1 (1965), 141–170

[44] R. S. Lashof (ed.), “Problems in diferential and algebraic topology”, Seattle Conference, 1963, Ann. of Math. (2), 81 (1965), 565–591 | DOI | MR | Zbl

[45] B. Mazur, “On embeddings of spheres”, Bull. Amer. Math. Soc., 65:1 (1959), 59–65 | DOI | MR | Zbl

[46] M. Brown, “A proof of the generalized Schoenflies theorem”, Bull. Amer. Math. Soc., 66:2 (1960), 74–76 | DOI | MR | Zbl

[47] R. H. Bing, “A decomposition of $E^3$ into points and tame arcs such that the decomposition space is topologically different from $E^3$”, Ann. of Math. (2), 65:3 (1957), 484–500 | DOI | MR | Zbl

[48] M. K. Fort, Jr, “A note concerning a decomposition space defined by Bing”, Ann. of Math. (2), 65:3 (1957), 501–504 | DOI | MR | Zbl

[49] R. H. Bing, “The Cartesian product of a certain nonmanifold and a line is $E^4$”, Ann. of Math. (2), 70:3 (1959), 399–412 | DOI | MR | Zbl

[50] R. Penrose, J. H. C. Whitehead, E. C. Zeeman, “Imbeddings of manifolds in Euclidean space”, Ann. of Math. (2), 73:3 (1961), 613–623 | DOI | MR | Zbl

[51] J. R. Stallings, “The piecewise-linear structure of Euclidean space”, Proc. Cambridge Philos. Soc., 58:3 (1962), 481–488 | DOI | MR | Zbl

[52] L. Keldysh, “Vlozhenie nulmernykh kompaktov v $E^n$”, Dokl. AN SSSR, 147:4 (1962), 772–775 | Zbl

[53] L. Keldysh, “Topologicheskie vlozheniya v mnogoobrazie i psevdoizotopiya”, Matem. sb., 71:4 (1966), 433–453 | MR | Zbl

[54] L. Keldysh, “Topologicheskie vlozheniya i psevdoizotopiya”, Dokl. AN SSSR, 169:6 (1966), 1262–1265 | MR | Zbl

[55] L. Keldysh, “O vlozhenii v $E^n$ i v $E^{n+1}$ nekotorykh monotonnykh obrazov $E^n$”, Matem. sb., 57:1 (1962), 95–104 | MR

[56] R. Yu. Matskina, “O topologicheskom vlozhenii prostranstva nepreryvnogo razbieniya $E^n$ na tochki i kompakty”, UMN, 20:6 (1965), 139–142 | MR | Zbl

[57] E. V. Sandrakova, “Vlozhenie nulmernykh kompaktov v $E^3$”, Matem. sb., 85:1 (1971), 98–114 | MR | Zbl

[58] Van Ni Kyong, “Vlozhenie odnogo nepreryvnogo razbieniya prostranstva $E^n$ v drugoe”, Matem. sb., 83:4 (1970), 547–555 | MR | Zbl

[59] Van Ni Kyong, “Psevdoizotopiya trekhmernoi sfery $S^3$”, Dokl. AN SSSR, 199:5 (1971), 1002–1003 | Zbl

[60] S. Armentrout, “Cellular decompositions of 3-manifolds that yield 3-manifolds”, Mem. Amer. Math. Soc., 107 (1971) | MR | Zbl

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[63] V. P. Kompaniets, A. V. Chernavskii, “Ekvivalentnost dvukh klassov otobrazhenii sfery”, Dokl. AN SSSR, 169:6 (1966), 1266–1268 | Zbl

[64] T. M. Price, “A necessary condition that a cellular upper semi-continuous decomposition of $E^n$ yield $E^n$”, Trans. Amer. Math. Soc., 122:2 (1966), 427–435 | DOI | MR | Zbl

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[66] R. C. Lacher, “Cellularity criteria for maps”, Michigan Math. J., 17:4 (1970), 385–396 | DOI | MR | Zbl

[67] S. Armentrout, T. M. Price, “Decompositions into compact sets with $UV$ properties”, Trans. Amer. Math. Soc., 141 (1969), 433–442 | DOI | MR | Zbl

[68] R. J. Daverman, Decomposition of Manifolds, Academic Press, Orlando, 1986 | MR | Zbl

[69] M. Brown, “Locally flat embeddings of topological manifolds”, Ann. of Math. (2), 75:2 (1962), 331–341 | DOI | MR | Zbl

[70] A. B. Sosinskii, “O vlozhenii $k$-mernogo elementa v $E^n$”, Dokl. AN SSSR, 139:6 (1961), 1311–1313 | MR | Zbl

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[75] H. Gluck, “Embeddings in the trivial range”, Ann. of Math. (2), 81:2 (1965), 195–210 | DOI | MR | Zbl

[76] A. V. Chernavskii, “Izotopiya elementov i sfer v $n$-mernom prostranstve pri $k\frac23n-1$”, Dokl. AN SSSR, 158:1 (1964), 62–65 | MR

[77] J. Alexander, “On the deformation of an $n$-cell”, Proc. Amer. Math. Soc., 9:3 (1923), 406–407 | Zbl

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[79] J. L. Bryant, C. L. Seebeck III, “Locally nice ebeddings in codimension three”, Bull. Amer. Math. Soc., 74:2 (1968), 378–380 | DOI | MR | Zbl

[80] A. V. Chernavskii, “Kusochno lineinaya approksimatsiya vlozhenii kletok i sfer v korazmernostyakh bolshikh dvukh”, Matem. sb., 80:3 (1969), 339–364 | MR

[81] R. T. Miller, “Approximating codimension 3 embeddings”, Ann. of Math. (2), 95:3 (1972), 406–416 | DOI | MR | Zbl

[82] A. V. Chernavskii, “Lokalno gomotopicheski nezauzlennye vlozheniya mnogoobrazii”, Dokl. AN SSSR, 181:2 (1968), 290–293 | MR

[83] A. V. Tschernawski, “Deckhomotopieeigenschaft in der Faserung der Homöomorphismengruppe über dem Raum der lokal flachen Einbettungen”, Theory of Sets and Topology, VEB Deutsch. Verlag Wissensch., Berlin, 1972, 503–508 | MR

[84] O. G. Harrold, Jr, “Euclidean domains with uniformly Abelian local fundamental groups”, Trans. Amer. Math. Soc., 67 (1949), 120–129 | DOI | MR | Zbl

[85] L. Keldysh, Topologicheskie vlozheniya v evklidovo prostranstvo, Tr. MIAN, 81, Nauka, M., 1966 | Zbl

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[87] L. C. Siebenmann, “Approximating cellular maps by homeomorphisms”, Topology, 11:3 (1972), 271–294 | DOI | MR | Zbl

[88] A. V. Chernavskii, “Sovpadenie lokalnoi ploskostnosti i lokalnoi odnosvyaznosti dlya vlozhenii $(n-1)$-mernykh mnogoobrazii v $n$-mernye pri $n>4$”, Matem. sb., 91:2 (1973), 279–286 | MR

[89] O. G. Harrold, “Locally peripherically Euclidean spaces are locally Eucldean”, Ann. of Math. (2), 74:2 (1961), 207–220 | DOI | MR | Zbl

[90] T. M. Price, C. L. Seebeck III, “Somewhere locally flat codimension one manifolds with 1$-$ULC complements are locally flat”, Trans. Amer. Math. Soc., 193:466 (1974), 111–122 | DOI | MR | Zbl

[91] R. Daverman, “Locally nice codimension one manifolds are locally flat”, Bull. Amer. Math. Soc., 79:2 (1973), 410–413 | DOI | MR | Zbl

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[94] J. C. Cantrell, “Non-flat embeddings of $S^{n-1}$ in $S^n$”, Michigan Math. J., 10:4 (1963), 359–362 | DOI | MR | Zbl

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[96] A. V. Chernavskii, “O $k$-stabilnosti gomeomorfizmov i ob'edinenii kletok”, Dokl. AN SSSR, 180:5 (1968), 1045–1047 | MR

[97] M. H. Freedman, “The topology of four-dimensional manifolds”, J. Differential Geom., 17:3 (1982), 357–453 | MR | Zbl

[98] A. B. Sosinskii, “Mnogomernye uzly”, Dokl. AN SSSR, 163:6 (1965), 1326–1329 | MR | Zbl

[99] A. B. Sosinskii, “Gomotopii dopolnenii k uzlam”, Dokl. AN SSSR, 176:6 (1967), 1258–1261 | MR | Zbl

[100] G. Ya. Zuev, A. B. Sosinskii, “O sferakh, soderzhaschikh nulmernye dikie mnozhestva”, Vestnik Mosk. un-ta. Ser. matem. mekh., 1967, no. 3, 5–9 | MR | Zbl

[101] T. Maeda, “On a composition of knot groups. II. Algebraic bridge index”, Math. Sem. Notes Koebe Univ., 5:3 (1977), 457–464 | MR | Zbl

[102] M. J. Dunwoody, R. A. Fenn, “On the finiteness of higher knot sums”, Topology, 26:3 (1987), 337–343 | DOI | MR | Zbl

[103] M. A. Shtanko, “Vlozhenie kompaktov v evklidovo prostranstvo”, Matem. sb., 83:2 (1970), 234–255 | MR | Zbl

[104] H. Bothe, “Ein eindimensionales Kompaktum in $E^3$, das sich nicht lagetreu in die Mengersche Universalkurve einbetten läßt”, Fund. Math., 54:3 (1964), 251–258 | MR | Zbl

[105] J. Bryant, “On embedding of compacta in Euclidean space”, Proc. Amer. Math. Soc., 23:1 (1969), 46–51 | DOI | MR | Zbl

[106] R. D. Edwards, “The topology of manifolds and cell-like maps”, Proceedings of International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, 111–127 | MR

[107] M. A. Shtanko, “Approksimatsiya kompaktov v $E^n$ v korazmernosti, bolshei dvukh”, Matem. sb., 90:4 (1973), 625–636 | MR | Zbl

[108] M. A. Shtanko, “Reshenie zadachi Mengera v klasse kompaktov”, Dokl. AN SSSR, 201:6 (1971), 1299–1302 | MR | Zbl

[109] H. Bothe, “Universalmengen bezüglich der Lage im $E^n$”, Fund. Math., 56:2 (1965), 203–212 | MR

[110] M. A. Shtanko, “Approksimatsiya vlozhenii mnogoobrazii v korazmernosti edinitsa”, Matem. sb., 94:3 (1974), 483–494 | MR | Zbl

[111] F. D. Ancel, J. W. Cannon, “The locally flat approximation of cell-like embedding relations”, Ann. of Math. (2), 109:1 (1979), 61–86 | DOI | MR | Zbl

[112] R. D. Edwards, “Demension theory. I”, Geometric Topology, Lecture Notes in Math., 438, Springer-Verlag, Berlin, 1975, 195–211 | MR

[113] J. L. Bryant, R. C. Lacher, “Resolving zero-dimensional singularities in generalized manifolds”, Math. Proc. Cambridge Philos. Soc., 83:3 (1978), 403–413 | DOI | MR | Zbl

[114] J. W. Cannon, J. L. Bryant, R. C. Lacher, “The structure of generalized manifolds having nonmanifold set of trivial dimension”, Geometric Topology: Proceedings of the Georgia Topology Conference (Athens, Ga, 1977), Academic Press, New York, 1979, 261–300 | MR

[115] A. V. Chernavskii, “Lokalnaya styagivaemost gruppy gomeomorfizmov mnogoobraziya”, Matem. sb., 79:3 (1969), 307–356 | MR

[116] M. Gromov, Partial Differential Relations, Springer-Verlag, Berlin, 1986 | MR

[117] B. Mazur, “The method of infinite repetition in pure topology. I”, Ann. of Math. (2), 80:2 (1964), 201–226 | DOI | MR | Zbl

[118] R. D. Edwards, R. C. Kirby, “Deformations of spaces of embeddings”, Ann. of Math. (2), 93:1 (1971), 63–88 | DOI | MR | Zbl

[119] M. Brown, H. Gluck, “Stable structures on manifolds. I. Homeomorphisms of $S^n$”, Ann. of Math. (2), 79:1 (1964), 1–17 | DOI | MR | Zbl

[120] R. C. Kirby, “Stable homeomorphisms and the annulus conjecture”, Ann. of Math. (2), 89 (1969), 575–582 | DOI | MR | Zbl

[121] F. Quinn, “The embedding theorems for towers”, Contemp. Math., 35 (1984), 461–471 | MR | Zbl

[122] R. D. Edwards, “The solution of the 4-dimensional annulus conjecture (after Frank Quinn)”, Contemp. Math., 35 (1984), 211–264 | MR | Zbl

[123] J. Kister, “Small isotopies in Euclidean spaces and 3-manifolds”, Bull. Amer. Math. Soc., 65:6 (1959), 371–373 | DOI | MR | Zbl

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