On the topological structure of compact 5-manifolds

Alberto Cavicchioli; Fulvia Spaggiari

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 513-524
  • ISSN: 0010-2628

Abstract

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We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let M be a closed connected orientable smooth 5 -manifold with free fundamental group. Then we prove that the number of distinct smooth 5 -manifolds homotopy equivalent to M equals the 2 -nd Betti number (mod 2 ) of M .

How to cite

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Cavicchioli, Alberto, and Spaggiari, Fulvia. "On the topological structure of compact 5-manifolds." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 513-524. <http://eudml.org/doc/247501>.

@article{Cavicchioli1993,
abstract = {We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let $M$ be a closed connected orientable smooth $5$-manifold with free fundamental group. Then we prove that the number of distinct smooth $5$-manifolds homotopy equivalent to $M$ equals the $2$-nd Betti number (mod $2$) of $M$.},
author = {Cavicchioli, Alberto, Spaggiari, Fulvia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {colored graph; crystallization; genus; manifold; surgery; s-cobordism; normal invariants; homotopy type; bundles over ; bundles over the 1-sphere; classification; free fundamental group; compact PL manifold; genus; smooth 5-manifolds},
language = {eng},
number = {3},
pages = {513-524},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the topological structure of compact 5-manifolds},
url = {http://eudml.org/doc/247501},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Cavicchioli, Alberto
AU - Spaggiari, Fulvia
TI - On the topological structure of compact 5-manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 513
EP - 524
AB - We classify the genus one compact (PL) 5-manifolds and prove some results about closed 5-manifolds with free fundamental group. In particular, let $M$ be a closed connected orientable smooth $5$-manifold with free fundamental group. Then we prove that the number of distinct smooth $5$-manifolds homotopy equivalent to $M$ equals the $2$-nd Betti number (mod $2$) of $M$.
LA - eng
KW - colored graph; crystallization; genus; manifold; surgery; s-cobordism; normal invariants; homotopy type; bundles over ; bundles over the 1-sphere; classification; free fundamental group; compact PL manifold; genus; smooth 5-manifolds
UR - http://eudml.org/doc/247501
ER -

References

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  10. Shaneson J.L., Wall’s surgery obstruction groups for G × ℤ , Ann. of Math. 90 (1969), 296-334. (1969) MR0246310
  11. Shaneson J.L., Non-simply connected surgery and some results in low dimension topology, Comm. Math. Helv. 45 (1970), 333-352. (1970) MR0275444
  12. Shaneson J.L., On non-simply connected manifolds, in Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, Rhode Island 22 (1970), 221-229. (1970) Zbl0226.57007MR0358816
  13. Smale S., On the structure of 5-manifolds, Ann. of Math. 75 (1962), 38-46. (1962) Zbl0101.16103MR0141133
  14. Wall C.T.C., Surgery on Compact Manifolds, Academic Press, London-New York, 1970. Zbl0935.57003MR0431216
  15. White A.T., Graphs, Groups and Surfaces, North Holland Ed., Amsterdam, 1973. Zbl0551.05037

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