대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제22권2호
  • /
  • Pages.289-295
  • /
  • 2007
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

PRODUCT OF PL FIBRATORS AS CODIMENSION-k FIBRATORS

  • Im, Young-Ho (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY) ;
  • Kim, Yong-Kuk (DEPARTMENT OF MATHEMATICS KYUNGPOOK NATIONAL UNIVERSITY)
  • 발행 : 2007.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We describe some conditions under which the product of two groups with certain property is a group with the same property, and we describe some conditions under which the product of hopfian manifolds is another hopfian manifold. As applications, we find some PL fibrators among the product of fibrators.

키워드

참고문헌

  1. D. S. Coram and P. F. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288 https://doi.org/10.1216/RMJ-1977-7-2-275
  2. D. S. Coram and P. F. Duvall, Approximate fibrations and a movability condition for maps, Pacific J. Math. 72 (1977), 41-56 https://doi.org/10.2140/pjm.1977.72.41
  3. R. J. Daverman, PL maps with manifold fibers, J. London Math. Soc. (2) 45 (1992), no. 1, 180-192 https://doi.org/10.1112/jlms/s2-45.1.180
  4. R. J. Daverman, Hyperhopfian groups and approximate fibrations, Compositio Math. 86 (1993), 159-176
  5. R. J. Daverman, Manifolds that induce approximate fibrations in the PL category, Topology Appl. 66 (1995), 267-297 https://doi.org/10.1016/0166-8641(95)00051-H
  6. R. J. Daverman, Codimension 2 nonfibrators with finite fundamental groups, Proc. Amer. Math. Soc. 127 (1999), no. 3, 881-888
  7. R. J. Daverman, Y. H. Im, and Y. Kim, Products of Hopfian manifolds and codimension-2 fibrators, Topology Appl. 103 (2000), no. 3, 323-338 https://doi.org/10.1016/S0166-8641(99)00008-5
  8. R. J. Daverman, Y. H. Im, and Y. Kim, Connected sums of 4-manifolds as codimension-k fibrators, J. London Math. Soc. (2) 68 (2003), no. 1, 206-222 https://doi.org/10.1112/S0024610703004332
  9. R. J. Daverman, Y. H. Im, and Y. Kim, PL fibrator properties of partially aspherical manifolds, Topology Appl. 140 (2004), no. 2-3, 181-195 https://doi.org/10.1016/j.topol.2003.07.016
  10. M. Hall, Subgroups of finite index in free groups, Canadian J. Math. 1 (1949), 187-190 https://doi.org/10.4153/CJM-1949-017-2
  11. J.-C. Hausmann, Geometric hopfian and non-hopfian situations, in Geometry and Topology (C. McCrory and T. Shifrin, eds.), Lecture Notes in Pure Appl. Math., Marcel Decker, Inc., New York, 1987, pp. 157-166
  12. S.-T. Hu, Homotopy Theory, Academic press (1959)
  13. Y. H. Im and Y. Kim, Necessary and suffient conditions for s-hopfian manifolds to be codimension-2 fibrators, Proc. Amer. Math. Soc. 129 (2001), no. 7, 2135-2140 https://doi.org/10.1090/S0002-9939-00-05998-0
  14. Y. Kim, Manifolds with hyperhopfian fundamental group as codimension-2 fibrators, Topology Appl. 96 (1999), 241-248 https://doi.org/10.1016/S0166-8641(98)00057-1
  15. W. Magnus, A. Karass, and D. Solitar, Combinatorial Group Theory, Dover Publ., Inc., New York, 1976
  16. S. Rosset, A vanishing theorem for Euler characteristics, Math. Z. 185 (1985), 211-215 https://doi.org/10.1007/BF01181691