Cubulations, immersions, mappability and a problem of Habegger
Funar, Louis
Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999), p. 681-700 / Harvested from Numdam
@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},
     volume = {32},
     year = {1999},
     pages = {681-700},
     doi = {10.1016/s0012-9593(01)80003-3},
     mrnumber = {2001f:57027},
     zbl = {0934.57027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1999_4_32_5_681_0}
}
Funar, Louis. Cubulations, immersions, mappability and a problem of Habegger. Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999) pp. 681-700. doi : 10.1016/s0012-9593(01)80003-3. http://gdmltest.u-ga.fr/item/ASENS_1999_4_32_5_681_0/

[Al] J.W. Alexander, The combinatorial theory of complexes. Annals of Math., 31 (1930), 292-320. | JFM 56.0497.02

[B] T. Banchoff, Triple points and surgery of immersed surfaces. Proc. Amer. Math. Soc., 46(1974), 407-413. | MR 51 #14066 | Zbl 0309.57017

[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 45 #7605 | Zbl 0221.52004

[B2] D.W. Barnette, A proof of the lower bound conjecture for convex polytopes. Pacific J. Math., 46(1973), 349-354. | MR 48 #7115 | Zbl 0264.52006

[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 82m:52006 | Zbl 0479.52006

[BB] G. Blind and R. Blind, Gaps in the number of faces of cubical polytopes. Discrete and Comp. Geometry, 11(1994), 351-356. | MR 95b:52014 | Zbl 0807.52009

[C1] J. Scott Carter, A further generalization of Boy's surface. Houston J. Math., 12(1986), 11-31. | MR 87j:57018 | Zbl 0639.57014

[C2] J. Scott Carter, Surgery on codimension-one immersions. Trans. Amer. Math. Soc., 298(1986), 83-101. | Zbl 0613.57012

[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 88a:57058 | Zbl 0664.55010

[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 88a:57033 | Zbl 0634.51012

[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 0645.55003

[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 0654.55005 | Zbl 0663.55005

[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 95e:57043 | Zbl 0880.57010

[E1] P.J. Eccles, Codimension 1 immersions and the Kervaire invariant one problem. Math. Proc. Cambridge Phil. Soc., 90(1981), 483-493. | MR 83c:57015 | Zbl 0479.57016

[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 0519.57024

[E3] P.J. Eccles, Multiple points of codimension-one immersions of oriented manifolds. Math. Proc. Cambridge Phil. Soc., 87(1980), 213-220. | MR 81j:55014 | Zbl 0472.57017

[F] M. Freedman, Quadruple points of 3-manifolds in S4. Comment. Math. Helvetici, 53(1978), 385-394. | MR 81b:57027 | Zbl 0404.57011

[Fun] L. Funar, Cubulations mod bubble moves. Contemporary Math. (to appear), 1998. | Zbl 0941.57023

[H] P.J. Herbert, Multiple points of immersed manifolds. Memoirs Amer. Math. Soc. 34, no. 250, 1981. | MR 84c:57022 | Zbl 0493.57012

[Hé] G. Hetyei, On the Stanley ring of a cubical complex. Discrete and Comp. Geometry, 14(1995), 305-330. | MR 96h:13060 | Zbl 0834.57015

[J] W. Jockusch, The lower and upper bound problems for cubical polytopes. Discrete and Comp. Geometry, 9(1993), 159-163. | MR 93j:52016 | Zbl 0771.52005

[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 92e:57037 | Zbl 0787.57017

[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 1470751 | Zbl 0888.57014

[Kos] U. Koschorke, Multiple points of immersions and the Kahn-Priddy theorem. Math. Z., 169(1979), 223-236. | MR 81a:57030 | Zbl 0406.57017

[KS] U. Koschorke and B. Sanderson, Selfintersections and higher Hopf invariants. Topology, 17(1978), 283-290. | MR 81i:55014 | Zbl 0398.57030

[L] J. Lannes, Sur les immersions de Boy. "Algebraic Topology", Aarhus, 1982, Lecture Notes Math., no. 1051, 263-270, 1984. | Zbl 0547.57024

[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 98m:57032 | Zbl 0889.57032

[Lick] R. Lickorish, Unshellable triangulations of spheres. European J. Combinatorics, 12(1991), 527-530. | MR 92k:57044 | Zbl 0746.57007

[Mcm] P. Mcmullen, On the number of faces of a simplicial polytope. Israel J. Math., 9(1971), 559-570. | MR 43 #3914 | Zbl 0209.53701

[Mcm2] P. Mcmullen, On simple polytopes. Inventiones Math., 113(1993), 419-444. | MR 94d:52015 | Zbl 0803.52007

[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 91f:52026 | Zbl 0698.52003

[P] U. Pachner, Homeomorphic manifolds are equivalent by elementary shellings. European J. Combinatorics, 12(1991), 129-145. | MR 92d:52040 | Zbl 0729.52003

[S] R. Stanley, The number of faces of a simplicial convex polytope. Advances Math., 35(1980), 236-238. | MR 81f:52014 | Zbl 0427.52006

[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 87a:52007 | Zbl 0573.52008

[Tu] V. Turaev, Quantum invariants of links and 3-valent graphs in 3-manifolds. De Gruyter Studies Math., vol. 18, 1994. | MR 95k:57014 | Zbl 0812.57003

[V] P. Vogel, Cobordisme d'immersions, Ann. Sci. École Norm. Sup. 7(1974), 317-358. | Numdam | MR 51 #9082 | Zbl 0302.57011