no. 5
Cubulations, immersions, mappability and a problem of Habegger
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 5, pp. 681-700. 
@article{ASENS_1999_4_32_5_681_0,
     author = {Funar, Louis},
     title = {Cubulations, immersions, mappability and a problem of {Habegger}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {681--700},
     publisher = {Elsevier},
     volume = {Ser. 4, 32},
     number = {5},
     year = {1999},
     doi = {10.1016/s0012-9593(01)80003-3},
     mrnumber = {2001f:57027},
     zbl = {0934.57027},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(01)80003-3/}
}
TY  - JOUR
AU  - Funar, Louis
TI  - Cubulations, immersions, mappability and a problem of Habegger
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1999
SP  - 681
EP  - 700
VL  - 32
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(01)80003-3/
DO  - 10.1016/s0012-9593(01)80003-3
LA  - en
ID  - ASENS_1999_4_32_5_681_0
ER  - 
%0 Journal Article
%A Funar, Louis
%T Cubulations, immersions, mappability and a problem of Habegger
%J Annales scientifiques de l'École Normale Supérieure
%D 1999
%P 681-700
%V 32
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(01)80003-3/
%R 10.1016/s0012-9593(01)80003-3
%G en
%F ASENS_1999_4_32_5_681_0
Funar, Louis. Cubulations, immersions, mappability and a problem of Habegger. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 5, pp. 681-700. doi : 10.1016/s0012-9593(01)80003-3. http://www.numdam.org/articles/10.1016/s0012-9593(01)80003-3/

[Al] J.W. Alexander, The combinatorial theory of complexes. Annals of Math., 31 (1930), 292-320. | JFM

[B] T. Banchoff, Triple points and surgery of immersed surfaces. Proc. Amer. Math. Soc., 46(1974), 407-413. | MR | Zbl

[BC] E.K. Babson and C.S. Chan, Counting faces of cubical spheres modulo two. Preprint, 1997.

[B1] D.W. Barnette, The minimum number of vertices of a simple polytope. Israel J. Math., 10(1971), 121-125. | MR | Zbl

[B2] D.W. Barnette, A proof of the lower bound conjecture for convex polytopes. Pacific J. Math., 46(1973), 349-354. | MR | Zbl

[BL] L.J. Billera and C.W. Lee, A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes. J. Combinatorial Theory, Ser. A, 31(1981), 237-255. | MR | Zbl

[BB] G. Blind and R. Blind, Gaps in the number of faces of cubical polytopes. Discrete and Comp. Geometry, 11(1994), 351-356. | MR | Zbl

[C1] J. Scott Carter, A further generalization of Boy's surface. Houston J. Math., 12(1986), 11-31. | MR | Zbl

[C2] J. Scott Carter, Surgery on codimension-one immersions. Trans. Amer. Math. Soc., 298(1986), 83-101. | Zbl

[C3] J. Scott Carter, On generalizing Boy's surface : Constructing a generator of the third stable stem. Trans. Amer. Math. Soc., 298(1986), 103-122. | MR | Zbl

[DSS1] N.P. Dolbilin, M.A. Shtan'Ko and M.I. Shtogrin, Cubic subcomplexes in regular lattices. Dokl. Akad. Nauk, SSSR, 291(1986), 277-279, translated in Soviet Math. Dokl., 34 (1987). | MR | Zbl

[DSS2] N.P. Dolbilin, M.A. Shtan'Ko and M.I. Shtogrin, A topology for the family of parameterizations of cycles modulo 2 in a three dimensional cubic lattice. Dokl. Akad. Nauk, SSSR, 295(1987), 19-23, translated in Soviet Math. Dokl., 36(1988). | Zbl

[DSS] N.P. Dolbilin, M.A. Shtan'Ko and M.I. Shtogrin, The problem of parameterizations of cycles modulo 2 in a three dimensional cubic lattice. Izv. Ross. Akad. Nauk, Ser. Mat., 52(1988), 355-377, translated in Russian Acad. Sci. Izvestya Math., 32(1989). | Zbl

[DSS3] N.P. Dolbilin, M.A. Shtan'Ko and M.I. Shtogrin, Cubic manifolds in lattices. Izv. Ross. Akad. Nauk, Ser. Mat., 58(1994), translated in Russian Acad. Sci. Izvestya Math., 44(1995), 301-313. | MR | Zbl

[E1] P.J. Eccles, Codimension 1 immersions and the Kervaire invariant one problem. Math. Proc. Cambridge Phil. Soc., 90(1981), 483-493. | MR | Zbl

[E2] P.J. Eccles, Multiple points of codimension 1 immersions. "Topology Symposium", Siegen 1979, (U. Koschorke and W. Neumann Eds.), Lecture Notes Math. no. 788, 23-38, 1980. | Zbl

[E3] P.J. Eccles, Multiple points of codimension-one immersions of oriented manifolds. Math. Proc. Cambridge Phil. Soc., 87(1980), 213-220. | MR | Zbl

[F] M. Freedman, Quadruple points of 3-manifolds in S4. Comment. Math. Helvetici, 53(1978), 385-394. | EuDML | MR | Zbl

[Fun] L. Funar, Cubulations mod bubble moves. Contemporary Math. (to appear), 1998. | Zbl

[H] P.J. Herbert, Multiple points of immersed manifolds. Memoirs Amer. Math. Soc. 34, no. 250, 1981. | MR | Zbl

[Hé] G. Hetyei, On the Stanley ring of a cubical complex. Discrete and Comp. Geometry, 14(1995), 305-330. | EuDML | MR | Zbl

[J] W. Jockusch, The lower and upper bound problems for cubical polytopes. Discrete and Comp. Geometry, 9(1993), 159-163. | EuDML | MR | Zbl

[Kara] O.R. Karalashvili, On mappings of cubic manifolds into the standard lattice of Euclidean space. Trudy Mat. Inst. Steklov, 196(1991), 86-89, translated in Proc. Steklov Inst. Math., 196(1992). | MR | Zbl

[Kirby] R. Kirby, Problems in low-dimensional topology. "Geometric Topology", Georgia International Topology Conference, (W.H. Kazez, Ed.), AMS-IP Studies in Advanced Math., vol. 2., part 1, 35-472, 1995. | MR | Zbl

[Kos] U. Koschorke, Multiple points of immersions and the Kahn-Priddy theorem. Math. Z., 169(1979), 223-236. | EuDML | MR | Zbl

[KS] U. Koschorke and B. Sanderson, Selfintersections and higher Hopf invariants. Topology, 17(1978), 283-290. | MR | Zbl

[L] J. Lannes, Sur les immersions de Boy. "Algebraic Topology", Aarhus, 1982, Lecture Notes Math., no. 1051, 263-270, 1984. | Zbl

[Li] R. Lickorish, Piecewise linear manifolds and Cerf theory. "Geometric Topology", Georgia International Topology Conference, (W.H. Kazez, Editor), AMS-IP Studies in Advanced Math., vol. 2., part 1, 375-387, 1995. | MR | Zbl

[Lick] R. Lickorish, Unshellable triangulations of spheres. European J. Combinatorics, 12(1991), 527-530. | MR | Zbl

[Mcm] P. Mcmullen, On the number of faces of a simplicial polytope. Israel J. Math., 9(1971), 559-570. | MR | Zbl

[Mcm2] P. Mcmullen, On simple polytopes. Inventiones Math., 113(1993), 419-444. | EuDML | MR | Zbl

[N] S.P. Novikov, Topology. Itogi Nauki i Tekhniki : Sovremennye Problemy Mat. : Fundamentl'nye Naprovleniya, vol. 12 VINITI Moscow, 1986, 5-252, translated in Encyclopaedia of Math. Sci., vol. 12, Topology I, Springer Verlag, Berlin, 1992.

[P1] U. Pachner, Shellings of simplicial balls and p.l. manifolds with boundary. Discrete Math., 81(1990), 37-47. | MR | Zbl

[P] U. Pachner, Homeomorphic manifolds are equivalent by elementary shellings. European J. Combinatorics, 12(1991), 129-145. | MR | Zbl

[S] R. Stanley, The number of faces of a simplicial convex polytope. Advances Math., 35(1980), 236-238. | MR | Zbl

[S2] R. Stanley, The number of faces of a simplicial polytopes and spheres. "Discrete Geometry and Convexity", (J.E. Goodman and all., Eds.), Annals of the N.Y. Academy of Sci., 440(1985), 212-223. | MR | Zbl

[Tu] V. Turaev, Quantum invariants of links and 3-valent graphs in 3-manifolds. De Gruyter Studies Math., vol. 18, 1994. | MR | Zbl

[V] P. Vogel, Cobordisme d'immersions, Ann. Sci. École Norm. Sup. 7(1974), 317-358. | EuDML | Numdam | MR | Zbl

Cité par Sources :