Homology lens spaces and Dehn surgery on homology spheres

Craig Guilbault

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 3, page 287-292
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Guilbault, Craig. "Homology lens spaces and Dehn surgery on homology spheres." Fundamenta Mathematicae 144.3 (1994): 287-292. <http://eudml.org/doc/212030>.

@article{Guilbault1994,
abstract = {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.},
author = {Guilbault, Craig},
journal = {Fundamenta Mathematicae},
keywords = {Dehn surgery; homology lens space; 3-manifold},
language = {eng},
number = {3},
pages = {287-292},
title = {Homology lens spaces and Dehn surgery on homology spheres},
url = {http://eudml.org/doc/212030},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Guilbault, Craig
TI - Homology lens spaces and Dehn surgery on homology spheres
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 3
SP - 287
EP - 292
AB - 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.
LA - eng
KW - Dehn surgery; homology lens space; 3-manifold
UR - http://eudml.org/doc/212030
ER -

References

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  1. [Co] M. M. Cohen, A Course in Simple Homotopy Theory, Springer, Berlin, 1973. Zbl0261.57009
  2. [Fu] S. Fukuhara, On an invariant of homology lens spaces, J. Math. Soc. Japan 36 (1984), 259-277. Zbl0527.57005
  3. [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. Zbl0713.57008
  4. [Ol] P. Olum, Mappings of manifolds and the notion of degree, Ann. of Math. 58 (1953), 458-480. Zbl0052.19901
  5. [Wa] F. Waldhausen, On mappings of handlebodies and of Heegard splittings, in: Topology of Manifolds, Markham, Chicago, 1970, 205-211. 

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