You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Manifolds with the Homotopy Type of Complex Projective Space
Transactions of the American Mathematical Society
Vol. 176 (Feb., 1973), pp. 165-180
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1996202
Page Count: 16
You can always find the topics here!Topics: Mathematical manifolds, Mathematics, Isomorphism, Sufficient conditions, Spheres, Mathematical problems, Data smoothing
Were these topics helpful?See something inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
It is known that in every even dimension greater than four there are infinitely many nonhomeomorphic smooth manifolds with the homotopy type of complex projective space. In this paper we provide an explicit construction of homotopy complex projective spaces. Our initial data will be a manifold X with the homotopy type of CP3 and an embedding γ3: S5 → S7. A homotopy 7-sphere Σ7 is constructed and an embedding γ4: Σ7 → S9 may be chosen. The procedure continues inductively until either an obstruction or the desired dimension is reached; in the latter case the final obstruction is the class of Σ2n - 1 in Θ2n - 1. Should this obstruction vanish, the final choice is of a diffeomorphism γn: Σ2n - 1 → S2n - 1. There results a manifold, denoted (X, γ3,⋯, γn - 1, γn), with the homotopy type of CPn. We describe the obstructions encountered, but are able to evaluate only the primary ones. It is shown that every homotopy complex projective space may be so constructed, and in terms of this construction, necessary and sufficient conditions for two homotopy complex projective spaces to be diffeomorphic are stated.
Transactions of the American Mathematical Society © 1973 American Mathematical Society