Embedding 3-manifolds and smooth structures of 4-manifolds

✍ Scribed by Fang Fuquan

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 719 KB
• Volume: 76
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00118-6

✦ Synopsis

Let M be a noncompact 4-manifold with at least two open ends. Suppose that one of these ends is homeomorphic to N x iI& where N is an oriented 3-manifold satisfying one of the following conditions:

(i) ~1 (N) is an extension of the free group by a perfect normal subgroup.

(ii) HI (N) g Z/n, @. @ Z/nk, k < 4, and the link form of N is isomorphic to (-!-) @. @ (+) where each n2, 1 < i < k, is a product of primes congruent to 1 (mod4).

(iii) HI (N) N Z/n, @ Z/n* and nz (i = 1,2) is a power of a prime congruent to 3 (mod 8).

Then there exist uncountably many different smooth 4-manifolds which are homeomorphic to M.