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.
Similar content being viewed by others
References
Banagl M. and Ranicki A. (2006). Generalized Arf invariants in algebraic L-theory. Adv. Math. 199: 542–668
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
Cappell S.E. (1974). Manifolds with fundamental group a generalized free product. I. Bull. Am. Math. Soc. 80: 1193–1198
Cappell S.E. (1974). On connected sums of manifolds. Topology 13: 395–400
Cappell S.E. (1974). Unitary nilpotent groups and Hermitian K-theory. I. Bull. Am. Math. Soc. 80: 1117–1122
Cappell S.E. (1976). A splitting theorem for manifolds. Invent. Math. 33(2): 69–170
Connolly, F.X., Davis, J.F.: The surgery obstruction groups of the infinite dihedral group. Geom. Topol. 8, 1043–1078 (electronic) (2004)
Connolly F. and Koźniewski T. (1995). Nil groups in K-theory and surgery theory. Forum Math. 7(1): 45–76
Connolly F.X. and Ranicki A.A. (2005). On the calculation of UNil. Adv. Math. 195: 205–258
Cappell S.E. and Shaneson J.L. (1971). On four dimensional surgery and applications. Comment. Math. Helv. 46: 500–528
Freedman, M.H., Quinn, F.: Topology of 4-manifolds. In: Princeton Mathematical Series, vol. 39. Princeton University Press, Princeton (1990)
Hempel, J.: 3-Manifolds. AMS Chelsea Publishing, Providence (2004) Reprint of the 1976 original
Jahren, B., Kwasik, S.: Manifolds homotopy equivalent to RP 4# RP 4. Math. Proc. Camb. Phil. Soc. 140, 245–252 (2006)
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
López~de Medrano, S.: Involutions on Manifolds. Springer, New York (1971). Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 59
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)
Ranicki, A.: Exact sequences in the algebraic theory of surgery. In: Mathematical Notes, vol. 26. Princeton University Press, Princeton (1981)
Stallings J. (1965). Whitehead torsion of free products. Ann. Math. 82(2): 354–363
Wall C.T.C. (1968). Free piecewise linear involutions on spheres. Bull. Am. Math. Soc. 74: 554–558
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
Weinberger S. (1987). On fibering four- and five-manifolds. Isr. J. Math. 59(1): 1–7
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by a grant from the National Science Foundation.
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-007-0099-x