Homology lens spaces and Dehn surgery on homology spheres

• Autorzy: Craig R. Guilbault
• Języki publikacji: EN

Abstrakty

EN

A homology lens space is a closed 3-manifold with ℤ-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space $M^3$ may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of $M^3$ is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer an alternative proof based on classical 3-manifold techniques.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57N10: Topology of general 3 -manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 3
• Strony: 287-292

Daty

wydano

1994

otrzymano

1993-08-24

Twórcy

autor

Craig R. Guilbault

• Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, U.S.A.

Bibliografia

• [Co] M. M. Cohen, A Course in Simple Homotopy Theory, Springer, Berlin, 1973.
• [Fu] S. Fukuhara, On an invariant of homology lens spaces, J. Math. Soc. Japan 36 (1984), 259-277.
• [L-S] E. Luft and D. Sjerve, Degree-1 maps into lens spaces and free cyclic actions on homology spheres, Topology Appl. 37 (1990), 131-136.
• [Ol] P. Olum, Mappings of manifolds and the notion of degree, Ann. of Math. 58 (1953), 458-480.
• [Wa] F. Waldhausen, On mappings of handlebodies and of Heegard splittings, in: Topology of Manifolds, Markham, Chicago, 1970, 205-211.