Manifolds homotopy equivalent to P n # P n

Abstract

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.

Smooth structures on nonorientable four-manifolds and free involutions

“…There exists a manifold that is homeomorphic but not diffeomorphic to Remark 32. There are infinitely many non-orientable closed topological 4-manifolds homotopy equivalent to a connected sum that are not homeomorphic to a trivial connected sum as in Item (5) of Theorem 3 [7,22,6]. It is proven in [24, Theorem 3.4] (cf.…”

Free involutions on S 1 × S n

“…The case R P n+1 # R P n+1 is in many ways the most interesting one, but it was treated in detail in [2] and [11], so except for a few comments in Sect. 3.2 we refer to these papers for precise statements.…”

“…These manifolds exist because of the appearence of large UN il-groups in these dimensions. For more precise statements and calculations, see [2]. (Note, however, that surprisingly little is known about the geometry of these manifolds, in particular for n = 3.…”

“…3). The case R P n+1 # R P n+1 (n even) is decided by the results of [2] (proof of Theorem 2). If n ≡ 0 mod 4 we can use reflection in R P n # R P n , but if n ≡ 2 mod 4 there is no such homeomorphism.…”

“…The problem addressed in A was solved in [5,6] and the classification of manifolds homotopy equivalent to R P n # R P n was achieved in [2], Theorem 2. (Cf.…”