Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IM2_2005_69_5_a1, author = {A. Yu. Volovikov}, title = {Coincidence points of maps of $\mathbb Z_p^n$-spaces}, journal = {Izvestiya. Mathematics }, pages = {913--962}, publisher = {mathdoc}, volume = {69}, number = {5}, year = {2005}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_5_a1/} }
A. Yu. Volovikov. Coincidence points of maps of $\mathbb Z_p^n$-spaces. Izvestiya. Mathematics , Tome 69 (2005) no. 5, pp. 913-962. http://geodesic.mathdoc.fr/item/IM2_2005_69_5_a1/
[1] Bogatyi S. A., “Tsiklicheskie sistemy, konfiguratsionnye prostranstva i teorema Borsuka–Ulama–Mankkholma–Fenna–Konneta–Koena–Laska”, Tr. Matem. in-ta im. V. A. Steklova, 212 (1996), 46–60 | MR
[2] Bogatyi S. A., “Gipoteza Borsuka, prepyatstvie Ryshkova, interpolyatsiya, chebyshevskie priblizheniya, transversalnaya teorema Tverberga, problemy”, Tr. Matem. in-ta im. V. A. Steklova, 239 (2002), 63–82 | MR | Zbl
[3] Bolotov D. V., “Gipoteza Koena–Laska”, Matem. zametki, 70:1 (2001), 22–26 | MR | Zbl
[4] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., “Topologicheskie metody v teorii nepodvizhnoi tochki mnogoznachnykh otobrazhenii”, UMN, 35:1 (1980), 59–126 | MR | Zbl
[5] Volovikov A. Yu., “Otobrazheniya svobodnykh $\mathbb Z_p$-prostranstv v mnogoobraziya”, Izv. AN SSSR. Ser. matem., 46:1 (1982), 36–55 | MR | Zbl
[6] Volovikov A. Yu., Otobrazheniya svobodnykh $\mathbb Z_p$-prostranstv v mnogoobraziya, Dis. ... kand. fiz.-mat. nauk, MGU, M., 1982
[7] Volovikov A. Yu., “K teoreme Yanga o funktsiyakh na sfere”, Tez. dokl. IX Vsesoyuznoi geometricheskoi konferentsii, Shtiintsa, Kishinev, 1988, 68–69 | MR
[8] Volovikov A. Yu., “Teorema Burzhena–Yanga dlya $\mathbb Z^n_p$-deistviya”, Matem. sb., 183:7 (1992), 115–144 | MR
[9] Volovikov A. Yu., “Ob otobrazheniyakh mnogoobrazii Shtifelya so svobodnym $\mathbb Z_p^n$-deistviem v mnogoobraziya”, UMN, 47:6 (1992), 27–56 | MR
[10] Volovikov A. Yu., “Ob ekvivariantnykh mnogoznachnykh otobrazheniyakh”, UMN, 49:4 (1994), 159–160 | MR | Zbl
[11] Volovikov A. Yu., “K teoreme van Kampena–Floresa”, Matem. zametki, 59:5 (1996), 663–670 | MR | Zbl
[12] Volovikov A. Yu., “Ob indekse $G$-prostranstv”, Matem. sb., 191:9 (2000), 3–22 | MR | Zbl
[13] Volovikov A. Yu., “Ob odnom svoistve funktsii na sfere”, Matem. zametki, 70:5 (2001), 679–690 | MR | Zbl
[14] Volovikov A. Yu., “Tochki sovpadeniya otobrazhenii $\mathbb Z_p^n$-prostranstv v CW-kompleksy”, UMN, 57:1 (2002), 153–154 | MR | Zbl
[15] Volovikov A. Yu., “Ekvivariantnye otobrazheniya i nekotorye zadachi geometrii vypuklykh mnozhestv”, Tr. Matem. in-ta im. V. A. Steklova, 239 (2002), 83–97 | MR | Zbl
[16] Volovikov A. Yu., Schepin E. V., “Antipody i vlozheniya”, Matem. sb., 196:1 (2005), 3–32 | MR | Zbl
[17] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya. Metody teorii gomologii, Nauka, M., 1984 | MR
[18] Sklyarenko E. G., “K teorii obobschennykh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 35:4 (1971), 831–843 | Zbl
[19] Stesin M. I., “Ob aleksandrovskikh poperechnikakh sharov”, DAN SSSR, 217:1 (1974), 31–33 | MR | Zbl
[20] Stinrod N., Epstein D., Kogomologicheskie operatsii, Nauka, M., 1983 | MR
[21] Shvarts A. S., “Nekotorye otsenki roda topologicheskogo prostranstva v smysle Krasnoselskogo”, UMN, 12:4 (1957), 209–214 | MR | Zbl
[22] Shvarts A. S., “Rod rassloennogo prostranstva”, Tr. MMO, 10, URSS, M., 1961, 217–272
[23] Shvarts A. S., “Rod rassloennogo prostranstva”, Tr. MMO, 11, URSS, M., 1962, 99–126 | Zbl
[24] Schepin E. V., “Ob odnoi probleme L. A. Tumarkina”, DAN SSSR, 217:1 (1974), 42–43 | Zbl
[25] Schepin E. V., “Myagkie otobrazheniya mnogoobrazii”, UMN, 39:5 (1984), 209–224 | MR | Zbl
[26] Aepli A., Akiyama Y., “Cohomology operations in Smith theory”, Ann. Scuola. Norm. Sup. Piza, 24 (1970), 741–833 | MR
[27] Björner A., Welker V., “The homology of "$k$-equal" manifolds and related partition lattices”, Adv. Math., 110:2 (1995), 277–313 | DOI | MR
[28] Borel A., “Sur la cohomologie des espaces fibrés principaux et des espaces homogenes de groupes de Lie compact”, Ann. of Math., 57 (1953), 115–207 | DOI | MR | Zbl
[29] Borel A., Seminar on transformation groups, Ann. of Math. Stud., 46, Princeton Univ. Press, Princeton–New Jersey, 1960 | MR | Zbl
[30] Bourgin D. G., “On some separation and mapping theorems”, Comment. Math. Helv., 29 (1955), 199–214 | DOI | MR | Zbl
[31] Bourgin D. G., “Multiplicity of solutions in frame mappings”, Illinois J. Math., 9 (1965), 169–177 | MR | Zbl
[32] Bredon G. E., Introduction to compact transformation groups, Academic Press, N. Y.–London, 1972 | MR | Zbl
[33] Bredon G., Sheaf theory, McGraw-Hill, N. Y., 1967 | MR | Zbl
[34] Chang T., Skjelbred T., “Group actions on Poincaré duality spaces”, Bull. Amer. Math. Soc., 78 (1972), 1024–1026 | DOI | MR | Zbl
[35] Clapp M., Puppe D., “Critical point theory with symmetries”, J. reine angew Math., 418 (1991), 1–29 | MR | Zbl
[36] Conner P. E., Floyd E. E., “Fixed point free involutions and equivariant maps”, Bull. Amer. Math. Soc., 66 (1960), 416–441 | DOI | MR | Zbl
[37] Conner P. E., Floyd E. E., “Fixed point free involutions and equivariant maps, II”, Trans. Amer. Math. Soc., 105 (1962), 222–228 | DOI | MR | Zbl
[38] Conner P. E., Floyd E. E., Differentiable periodic maps, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1964 | MR | Zbl
[39] Cohen F., Lusk E. L., “Coincidence point results for spaces with free $\mathbb Z_p$-actions”, Proc. Amer. Math. Soc., 49:1 (1975), 245–252 | DOI | MR | Zbl
[40] Cohen F., Lusk E. L., “Configuration-like spaces and the Borsuk–Ulam theorem”, Proc. Amer. Math. Soc., 56 (1976), 313–317 | DOI | MR | Zbl
[41] Tom Dieck T., Transformation groups, Walter de Gruyter, Berlin–N. Y., 1987 | MR | Zbl
[42] Fadell E., Husseini S., “An ideal-valued cohomological index theory with applications to Borsuk–Ulam and Bourgin–Yang theorems”, Ergodic theory and dynamic systems, 8, Spec. Issue (1988), 259–268 | MR
[43] Flores A., “Über $n$-dimensionale Komplexe die im $R_{2n+1}$ absolut selbstverschlungen sind”, Ergegb. Math. Kolloq., 6 (1933/34), 4–7
[44] Goncalves D. L., Pergher P. Q. L., “$\mathbb Z_p$-coincidences for maps of spheres into CW complexes”, Kobe J. Math., 15:1 (1998), 191–195 | MR | Zbl
[45] Goncalves D. L., Jaworowski J., Pergher P. Q. L., “G-coincidences for maps of homotopy spheres into CW complexes”, Proc. Amer. Math. Soc., 130:10 (2002), 3111–3115 | DOI | MR | Zbl
[46] Goncalves D. L., Jaworowski J., Pergher P. Q. L., “Measuring the size of the coincidence set”, Topology Appl., 125:3 (2002), 465–470 | DOI | MR | Zbl
[47] Goncalves D. L., Jaworowski J., Pergher P. Q. L., Volovikov A. Yu., “Coincidences for maps of spaces with finite group actions”, Topology Appl., 145:1–3 (2004), 61–68 | DOI | MR | Zbl
[48] Hopf H., “Freie Überdeckungen und frei Abbildungen”, Fund. Math., 28 (1937), 33–57 | Zbl
[49] Hopf H., “Verallgemeinerung bekannter Abildungs- und Überdeckungssätze”, Port. Math., 4 (1943/44), 129–139 | MR
[50] Hsiang W. Y., Cohomological theory of topological transformation groups, Springer-Verlag, Berlin–Heidelberg–N. Y., 1975 | MR
[51] Izydorek M., Jaworowski J., “Antipodal coincidence for maps of spheres into complexes”, Proc. Amer. Math. Soc., 123 (1995), 1947–1950 | DOI | MR | Zbl
[52] Jaworowski J., “Periodic coincidence for maps of spheres”, Kobe J. Math., 17 (2000), 21–26 | MR | Zbl
[53] Kakutani S., “A proof that there exists a circumscribing cube around any bounded closed convex set in $\mathbb R^3$”, Ann. of Math. (2), 43 (1942), 739–741 | DOI | MR | Zbl
[54] Li C. Q., “On solutions of frame mappings into manifolds”, Lect. Notes in Math., 1411, 1989, 143–147 | MR
[55] Lusk E. L., “The mod $p$ Smith index and a generalized Borsuk–Ulam theorem”, Mich. Math. J., 22 (1975), 151–160 | DOI | MR | Zbl
[56] Matousek J., Using the Borsuk–Ulam Theorem. Lectures on Topological Methods in Combinatorics and Geometry, Springer-Verlag, Berlin–Heidelberg–N. Y., 2003 | MR
[57] Munkholm H. J., “On the Borsuk–Ulam theorem for $\mathbb Z_{p^\alpha}$ actions on $S^{2n-1}$ and maps $S^{2n-1}\to\mathbb R^m$”, Osaka J. Math., 7 (1970), 451–456 | MR | Zbl
[58] Scordev G. S., “On a theorem of H. Hopf”, Serdica. Bulg. math. publ., 1 (1975), 317–325 | MR
[59] Stefanov S. T., “Mapping theorems for $\mathbb Z_p$-actions with fixed points”, Serdica. Bulg. math. publ., 16 (1990), 87–93 | MR | Zbl
[60] Stefanov S. T., “Yang index of the deleted product”, Proc. Amer. Math. Soc., 128:3 (1999), 885–891 | DOI | MR
[61] Väisälä J., “A theorem of the Borsuk–Ulam type for maps into non-manifolds”, Topology, 20 (1981), 319–322 | DOI | MR
[62] Volovikov A., “Mappings of free $\mathbb Z_p$-spaces into manifolds”, Leningrad International Topological Conference. Abstracts, Nauka, Leningrad, 1982, 168 | MR
[63] Volovikov A., Dimension and C-essentiality of the set of $Z_p$-coincidences of map, Abstracts of the Second Soviet-Japanese Symposium on Dimension and related Topics. Preprint No 7, MIAN SSSR, 1989, p. 55
[64] Volovikov A., “Dimension and $C$-essentiality of $\mathbb Z_p$-coincidence set of map”, $Q$ $A$ in General Topology, 8, Spec. Issue (1990), 207–217 | MR | Zbl
[65] Wu W.-T., A theory of imbedding, immersion, and isotopy of polytopes in a Euclidean space, Science press, Peking, 1965 | MR
[66] Yamabe H., Yujobô Z., “On the continuous functions defined on a sphere”, Osaka Math. J., 2:1 (1950), 19–22 | MR | Zbl
[67] Yang C. T., “On theorems of Borsuk–Ulam, Kakutani–Yamabe–Yujobô and Dyson, I”, Ann. of Math., 60 (1954), 262–282 | DOI | MR | Zbl
[68] Yang C. T., “Continuous functions from spheres to Euclidean spaces”, Ann. of Math., 62:2 (1955), 284–292 | DOI | MR | Zbl
[69] Yang C. T., “On maps from spheres to Euclidean spaces”, Amer. J. Math., 79 (1957), 725–732 | DOI | MR | Zbl
[70] Z̆ivaljević R. T., “User's guide to equivariant methods in combinatorics”, Publications of the Institute of Mathematics. Belgrade, 59 (73) (1996), 114–130 | MR | Zbl