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Annals of Mathematics, II. Series Vol. 149, No. 3, pp. 707754 (1999) 

Surgery and dualityMatthias KreckReview from Zentralblatt MATH: This paper describes a new context in which to do surgery on manifolds. As the author describes it in rough terms, one compares $n$dimensional manifolds with a topological space having a chosen $k$skeleton for some $k\geq [n/2]$. A bit more precisely, one begins with a map $B\to BO$ and does surgery on maps $M \to B$ classifying the normal bundle with $M$ homotopy equivalent to $B$ up to dimension $k$. The initial example is the classification of complete intersections of complex dimension $n$ for which $B$ looks like $CP^\infty$ up to dimension $n$. Other specific applications are given for 4dimensional topological manifolds which are Spin and have $\pi_1= Z$ and for simply connected 7dimensional homogeneous spaces. A sample of a good general result is that two closed $2q$dimensional manifolds with the same Euler characteristic and same normal $(q1)$type admitting bordant normal $(q1)$smoothings are diffeomorphic after taking the connected sum with some copies of $S^q\times S^q$. Reviewed by R.E.Stong Keywords: classification of complete intersections Classification (MSC2000): 57R65 57N13 57N15 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
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