Codimension 2 nonfibrators with finite fundamental groups

Daverman, R.

doi:10.1090/S0002-9939-99-05192-8

Codimension 2 nonfibrators with finite fundamental groups
HTML articles powered by AMS MathViewer

by R. J. Daverman

Proc. Amer. Math. Soc. 127 (1999), 881-888

DOI: https://doi.org/10.1090/S0002-9939-99-05192-8

PDF | Request permission

Abstract:

Fibrators are $n$-manifolds which automatically induce approximate fibrations, in the following sense: given any proper mapping $p$ from an $(n+k)$-manifold onto a finite-dimensional metric space such that, up to shape, each point-preimage is a copy of the fibrator, $p$ is necessarily an approximate fibration. This paper sets forth new examples, for the case $k=2$, of nonfibrators whose fundamental groups are finite.

References

N. Chinen, Manifolds with nonzero Euler characteristic and codimension $2$ fibrators, Topology Appl. 86 (1998), 151–167.
, Finite groups and approximate fibrations, preprint.
Marshall M. Cohen, A course in simple-homotopy theory, Graduate Texts in Mathematics, Vol. 10, Springer-Verlag, New York-Berlin, 1973. MR 0362320, DOI 10.1007/978-1-4684-9372-6
D. S. Coram and P. F. Duvall Jr., Approximate fibrations, Rocky Mountain J. Math. 7 (1977), no. 2, 275–288. MR 442921, DOI 10.1216/RMJ-1977-7-2-275
Donald Coram and Paul Duvall, Approximate fibrations and a movability condition for maps, Pacific J. Math. 72 (1977), no. 1, 41–56. MR 467745, DOI 10.2140/pjm.1977.72.41
D. Coram and P. Duvall, Nondegenerate $k$-sphere mappings between spheres, Topology Proc. 4 (1979), no. 1, 67–82 (1980). MR 583689
R. J. Daverman, Decompositions into codimension two submanifolds: the nonorientable case, Topology Appl. 24 (1986), no. 1-3, 71–81. Special volume in honor of R. H. Bing (1914–1986). MR 872479, DOI 10.1016/0166-8641(86)90050-7
R. J. Daverman, Submanifold decompositions that induce approximate fibrations, Topology Appl. 33 (1989), no. 2, 173–184. MR 1020279, DOI 10.1016/S0166-8641(89)80006-9
Robert J. Daverman, Manifolds with finite first homology as codimension $2$ fibrators, Proc. Amer. Math. Soc. 113 (1991), no. 2, 471–477. MR 1086581, DOI 10.1090/S0002-9939-1991-1086581-0
Robert J. Daverman, $3$-manifolds with geometric structure and approximate fibrations, Indiana Univ. Math. J. 40 (1991), no. 4, 1451–1469. MR 1142723, DOI 10.1512/iumj.1991.40.40065
R. J. Daverman, Hyper-Hopfian groups and approximate fibrations, Compositio Math. 86 (1993), no. 2, 159–176. MR 1214455
R. J. Daverman and J. J. Walsh, Decompositions into codimension-two manifolds, Trans. Amer. Math. Soc. 288 (1985), no. 1, 273–291. MR 773061, DOI 10.1090/S0002-9947-1985-0773061-4
Charles H. Giffen, The generalized Smith conjecture, Amer. J. Math. 88 (1966), 187–198. MR 198462, DOI 10.2307/2373054
Young Ho Im, Products of surfaces that induce approximate fibrations, Houston J. Math. 21 (1995), no. 2, 339–348. MR 1342414
R. C. Kirby and L. C. Siebenmann, Normal bundles for codimension $2$ locally flat imbeddings, Geometric topology (Proc. Conf., Park City, Utah, 1974) Lecture Notes in Math., Vol. 438, Springer, Berlin, 1975, pp. 310–324. MR 0400237
C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744, DOI 10.1007/978-3-642-81735-9
E. C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471–495. MR 195085, DOI 10.1090/S0002-9947-1965-0195085-8