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Free involutions on S 2 × S 3

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Abstract

In this paper, we classify smooth 5-manifolds with fundamental group isomorphic to \({\mathbb{Z}/2}\) and universal cover diffeomorphic to S 2 × S 3. This gives a classification of smooth free involutions on S 2 × S 3 up to conjugation.

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References

  1. Anderson D.W., Brown E.H., Peterson F.P.: The structure of the spin cobordism ring. Ann. Math. 86(2), 271–298 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baues, H.J.: Obstruction Theory on Homotopy Classification of Maps, Lecture Notes in Mathematics, vol. 628, Springer, New York (1977)

  3. Brown, K.S.: Cohomology of Groups, Graduate Texts in Mathematics, vol. 87, Springer, New York (1982)

  4. Geiges H., Thomas C.B.: Contact topology and the structure of 5-manifolds. Ann. Inst. Fourier 48, 1167–1188 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Haefliger A.: Differentiable imbeddings. Bull. Am. Math. Soc. 67, 109–112 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hambleton I.: Free involutions on 5-maniofolds. Indiana Univ. Math. J. 26(4), 777–787 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hambleton I., Kreck M.: On the classification of topological 4-manifolds with finite fundamental group. Math. Ann. 280, 85–104 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hambleton I., Kreck M., Teichner P.: Nonorientable 4-manifolds with fundamental group of order 2. Trans. Am. Math. Soc. 344, 649–665 (1944)

    MathSciNet  Google Scholar 

  9. Hambleton, I., Su, Y.: On certain 5-manifolds with fundamental group of order 2, arXiv:0903.5244v4

  10. Jahren, B., Kwasik, S.: Free invoultions on S 1 × S n, arXiv:0802.2035v1

  11. Kirby, R.C., Taylor, L.R.: Pin-structures on low-dimensional manifolds, geometry of low-dimensional Manifolds, 2. In: Donaldson, S.K., Thomas, C.B. (eds.) London Mathematical Society, Lecture Note Series, vol 151, Cambridge University Press, London (1989)

  12. Kreck, M.: An extension of results of Browder, Novikov and Wall about surgery on compact manifolds, Mainz preprint: available http://www.map.him.uni-bonn.de (1985)

  13. Kreck M.: Surgery and duality. Ann. Math. 149(2), 707–754 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lopez de Medrano S.: Involutions on Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 59. Springer, New York (1971)

    Google Scholar 

  15. Milnor J.: Whitehead torsion. Bull. Am. Math. Soc. 72, 358–426 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  16. Olbermann, M.: Conjugations on 6-Manifolds, Ph.D. Thesis, University of Heidelberg (2007) available http://www.ub.uni-heidelberg.de/archiv/7450/

  17. Sady R.: Free involutions on complex projective spaces. Michigan Math. J. 24, 51–64 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  18. Smale S.: On the structure of 5-manifolds. Ann. Math. 75(2), 38–46 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  19. Teichner P.: On the signature of four-manifolds with universal covering spin. Math. Ann. 295(4), 745–759 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wall C.T.C.: Surgery of non-simply-connected manifolds. Ann. Math. 84(2), 217–276 (1966)

    Article  MATH  Google Scholar 

  21. Wall, C.T.C.: Surgery on compact manifolds. In: A. A. Ranicki (ed.) Mathematical Surveys and Monographs. vol. 69, 2nd edn. American Mathematical Society, Providence, RI (1999)

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  1. Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China

    Yang Su

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  1. Yang Su
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Correspondence to Yang Su.

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Su, Y. Free involutions on S 2 × S 3 . Geom Dedicata 159, 11–28 (2012). https://doi.org/10.1007/s10711-011-9642-8

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Mathematics Subject Classification (2000)

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