Cubulations, immersions, mappability and a problem of Habegger

Louis Funar

Annales scientifiques de l'École Normale Supérieure (1999)

  • Volume: 32, Issue: 5, page 681-700
  • ISSN: 0012-9593

How to cite

top

Funar, Louis. "Cubulations, immersions, mappability and a problem of Habegger." Annales scientifiques de l'École Normale Supérieure 32.5 (1999): 681-700. <http://eudml.org/doc/82498>.

@article{Funar1999,
author = {Funar, Louis},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {cubical decomposition; immersions; triangulation; cubulation},
language = {eng},
number = {5},
pages = {681-700},
publisher = {Elsevier},
title = {Cubulations, immersions, mappability and a problem of Habegger},
url = {http://eudml.org/doc/82498},
volume = {32},
year = {1999},
}

TY - JOUR
AU - Funar, Louis
TI - Cubulations, immersions, mappability and a problem of Habegger
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1999
PB - Elsevier
VL - 32
IS - 5
SP - 681
EP - 700
LA - eng
KW - cubical decomposition; immersions; triangulation; cubulation
UR - http://eudml.org/doc/82498
ER -

References

top
  1. [Al] J.W. ALEXANDER, The combinatorial theory of complexes. Annals of Math., 31 (1930), 292-320. Zbl56.0497.02JFM56.0497.02
  2. [B] T. BANCHOFF, Triple points and surgery of immersed surfaces. Proc. Amer. Math. Soc., 46(1974), 407-413. Zbl0309.57017MR51 #14066
  3. [BC] E.K. BABSON and C.S. CHAN, Counting faces of cubical spheres modulo two. Preprint, 1997. Zbl0947.52004
  4. [B1] D.W. BARNETTE, The minimum number of vertices of a simple polytope. Israel J. Math., 10(1971), 121-125. Zbl0221.52004MR45 #7605
  5. [B2] D.W. BARNETTE, A proof of the lower bound conjecture for convex polytopes. Pacific J. Math., 46(1973), 349-354. Zbl0264.52006MR48 #7115
  6. [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. Zbl0479.52006MR82m:52006
  7. [BB] G. BLIND and R. BLIND, Gaps in the number of faces of cubical polytopes. Discrete and Comp. Geometry, 11(1994), 351-356. Zbl0807.52009MR95b:52014
  8. [C1] J. SCOTT CARTER, A further generalization of Boy's surface. Houston J. Math., 12(1986), 11-31. Zbl0639.57014MR87j:57018
  9. [C2] J. SCOTT CARTER, Surgery on codimension-one immersions. Trans. Amer. Math. Soc., 298(1986), 83-101. Zbl0613.57012
  10. [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. Zbl0664.55010MR88a:57058
  11. [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). Zbl0634.51012MR88a:57033
  12. [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). Zbl0645.55003
  13. [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). Zbl0663.55005
  14. [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. Zbl0880.57010MR95e:57043
  15. [E1] P.J. ECCLES, Codimension 1 immersions and the Kervaire invariant one problem. Math. Proc. Cambridge Phil. Soc., 90(1981), 483-493. Zbl0479.57016MR83c:57015
  16. [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. Zbl0519.57024
  17. [E3] P.J. ECCLES, Multiple points of codimension-one immersions of oriented manifolds. Math. Proc. Cambridge Phil. Soc., 87(1980), 213-220. Zbl0472.57017MR81j:55014
  18. [F] M. FREEDMAN, Quadruple points of 3-manifolds in S4. Comment. Math. Helvetici, 53(1978), 385-394. Zbl0404.57011MR81b:57027
  19. [Fun] L. FUNAR, Cubulations mod bubble moves. Contemporary Math. (to appear), 1998. Zbl0941.57023
  20. [H] P.J. HERBERT, Multiple points of immersed manifolds. Memoirs Amer. Math. Soc. 34, no. 250, 1981. Zbl0493.57012MR84c:57022
  21. [Hé] G. HETYEI, On the Stanley ring of a cubical complex. Discrete and Comp. Geometry, 14(1995), 305-330. Zbl0834.57015MR96h:13060
  22. [J] W. JOCKUSCH, The lower and upper bound problems for cubical polytopes. Discrete and Comp. Geometry, 9(1993), 159-163. Zbl0771.52005MR93j:52016
  23. [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). Zbl0787.57017MR92e:57037
  24. [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. Zbl0888.57014MR1470751
  25. [Kos] U. KOSCHORKE, Multiple points of immersions and the Kahn-Priddy theorem. Math. Z., 169(1979), 223-236. Zbl0406.57017MR81a:57030
  26. [KS] U. KOSCHORKE and B. SANDERSON, Selfintersections and higher Hopf invariants. Topology, 17(1978), 283-290. Zbl0398.57030MR81i:55014
  27. [L] J. LANNES, Sur les immersions de Boy. "Algebraic Topology", Aarhus, 1982, Lecture Notes Math., no. 1051, 263-270, 1984. Zbl0547.57024
  28. [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. Zbl0889.57032MR98m:57032
  29. [Lick] R. LICKORISH, Unshellable triangulations of spheres. European J. Combinatorics, 12(1991), 527-530. Zbl0746.57007MR92k:57044
  30. [Mcm] P. MCMULLEN, On the number of faces of a simplicial polytope. Israel J. Math., 9(1971), 559-570. Zbl0209.53701MR43 #3914
  31. [Mcm2] P. MCMULLEN, On simple polytopes. Inventiones Math., 113(1993), 419-444. Zbl0803.52007MR94d:52015
  32. [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. 
  33. [P1] U. PACHNER, Shellings of simplicial balls and p.l. manifolds with boundary. Discrete Math., 81(1990), 37-47. Zbl0698.52003MR91f:52026
  34. [P] U. PACHNER, Homeomorphic manifolds are equivalent by elementary shellings. European J. Combinatorics, 12(1991), 129-145. Zbl0729.52003MR92d:52040
  35. [S] R. STANLEY, The number of faces of a simplicial convex polytope. Advances Math., 35(1980), 236-238. Zbl0427.52006MR81f:52014
  36. [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. Zbl0573.52008MR87a:52007
  37. [Tu] V. TURAEV, Quantum invariants of links and 3-valent graphs in 3-manifolds. De Gruyter Studies Math., vol. 18, 1994. Zbl0812.57003MR95k:57014
  38. [V] P. VOGEL, Cobordisme d'immersions, Ann. Sci. École Norm. Sup. 7(1974), 317-358. Zbl0302.57011MR51 #9082

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.