Contractibly embedded $2$-spheres in $S^{2}\times S^{2}$
HTML articles powered by AMS MathViewer
- by Youn W. Lee PDF
- Proc. Amer. Math. Soc. 85 (1982), 280-282 Request permission
Abstract:
We construct contractibly embedded $2$-spheres in ${S^2} \times {S^2}$ but not contained in a $4$-ball.References
-
E. Artin, Zur Isotopic zweidimensionaler Flächen in ${R_4}$, Hamburg Abh. 4 (1925), 174-177.
A. Babakhanian, Cohomological methods in group theory, Marcel, New York, 1972.
- Heinz Hopf, Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1942), 257–309 (German). MR 6510, DOI 10.1007/BF02565622
- Robion Kirby, A calculus for framed links in $S^{3}$, Invent. Math. 45 (1978), no. 1, 35–56. MR 467753, DOI 10.1007/BF01406222
- Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
- William S. Massey, Algebraic topology: An introduction, Harcourt, Brace & World, Inc., New York, 1967. MR 0211390
- John Milnor, Groups which act on $S^n$ without fixed points, Amer. J. Math. 79 (1957), 623–630. MR 90056, DOI 10.2307/2372566
- Louise Moser, Elementary surgery along a torus knot, Pacific J. Math. 38 (1971), 737–745. MR 383406, DOI 10.2140/pjm.1971.38.737
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Joseph J. Rotman, Notes on homological algebras, Van Nostrand Reinhold Mathematical Studies, No. 26, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. MR 0409590
- H. Seifert, Topologie Dreidimensionaler Gefaserter Räume, Acta Math. 60 (1933), no. 1, 147–238 (German). MR 1555366, DOI 10.1007/BF02398271
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- John Stallings, Homology and central series of groups, J. Algebra 2 (1965), 170–181. MR 175956, DOI 10.1016/0021-8693(65)90017-7
- E. C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc. 115 (1965), 471–495. MR 195085, DOI 10.1090/S0002-9947-1965-0195085-8
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 280-282
- MSC: Primary 57Q45; Secondary 57R60
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652458-X
- MathSciNet review: 652458