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Manifolds homotopy equivalent to P n # P n

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Abstract

We classify, up to homeomorphism, all closed manifolds having the homotopy type of a connected sum of two copies of real projective n-space.

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References

  1. Banagl M. and Ranicki A. (2006). Generalized Arf invariants in algebraic L-theory. Adv. Math. 199: 542–668

    Article  MATH  MathSciNet  Google Scholar 

  2. Brookman, J.G.: Splitting homotopy equivalences along codimension 1 submanifolds. Ph.D. Thesis, University of Edinburgh (2004). http://www.jbrookman.me.uk/surgery/thesis.pdf

  3. Cappell S.E. (1974). Manifolds with fundamental group a generalized free product. I. Bull. Am. Math. Soc. 80: 1193–1198

    MATH  MathSciNet  Google Scholar 

  4. Cappell S.E. (1974). On connected sums of manifolds. Topology 13: 395–400

    Article  MATH  MathSciNet  Google Scholar 

  5. Cappell S.E. (1974). Unitary nilpotent groups and Hermitian K-theory. I. Bull. Am. Math. Soc. 80: 1117–1122

    MATH  MathSciNet  Google Scholar 

  6. Cappell S.E. (1976). A splitting theorem for manifolds. Invent. Math. 33(2): 69–170

    Article  MATH  MathSciNet  Google Scholar 

  7. Connolly, F.X., Davis, J.F.: The surgery obstruction groups of the infinite dihedral group. Geom. Topol. 8, 1043–1078 (electronic) (2004)

    Google Scholar 

  8. Connolly F. and Koźniewski T. (1995). Nil groups in K-theory and surgery theory. Forum Math. 7(1): 45–76

    Article  MATH  MathSciNet  Google Scholar 

  9. Connolly F.X. and Ranicki A.A. (2005). On the calculation of UNil. Adv. Math. 195: 205–258

    Article  MATH  MathSciNet  Google Scholar 

  10. Cappell S.E. and Shaneson J.L. (1971). On four dimensional surgery and applications. Comment. Math. Helv. 46: 500–528

    Article  MATH  MathSciNet  Google Scholar 

  11. Freedman, M.H., Quinn, F.: Topology of 4-manifolds. In: Princeton Mathematical Series, vol. 39. Princeton University Press, Princeton (1990)

  12. Hempel, J.: 3-Manifolds. AMS Chelsea Publishing, Providence (2004) Reprint of the 1976 original

  13. Jahren, B., Kwasik, S.: Manifolds homotopy equivalent to RP 4# RP 4. Math. Proc. Camb. Phil. Soc. 140, 245–252 (2006)

  14. Kirby, R.C., Siebenmann, L.C.: Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton University Press, Princeton (1977). With notes by John Milnor and Michael Atiyah, Annals of Mathematics Studies, No. 88

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

  16. Lück, W.: K- and L-theory of the semi-direct product of the discrete Heisenberg group by Z/4. Geom. Topol. 9, 1639–1676 (electronic) (2005)

    Google Scholar 

  17. Ranicki, A.: Exact sequences in the algebraic theory of surgery. In: Mathematical Notes, vol. 26. Princeton University Press, Princeton (1981)

  18. Stallings J. (1965). Whitehead torsion of free products. Ann. Math. 82(2): 354–363

    Article  MathSciNet  Google Scholar 

  19. Wall C.T.C. (1968). Free piecewise linear involutions on spheres. Bull. Am. Math. Soc. 74: 554–558

    Article  MATH  MathSciNet  Google Scholar 

  20. Wall, C.T.C.: Surgery on compact manifolds. In: Mathematical Surveys and Monographs, vol. 69, 2nd edn. American Mathematical Society, Providence (1999). Edited and with a foreword by A. A. Ranicki

  21. Weinberger S. (1987). On fibering four- and five-manifolds. Isr. J. Math. 59(1): 1–7

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Jeremy Brookman, James F. Davis & Qayum Khan

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  1. Jeremy Brookman
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  2. James F. Davis
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  3. Qayum Khan
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Corresponding author

Correspondence to James F. Davis.

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Partially supported by a grant from the National Science Foundation.

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Brookman, J., Davis, J.F. & Khan, Q. Manifolds homotopy equivalent to P n # P n . Math. Ann. 338, 947–962 (2007). https://doi.org/10.1007/s00208-007-0099-x

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  • DOI: https://doi.org/10.1007/s00208-007-0099-x

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