# Exotic smooth structures on 4-manifolds

#### Abstract

Let X be a compact smooth connected 4-manifold. Suppose $\pi\sb1$X has an orientation reversing element of order 2. Suppose A$\in$ GL(3,Z) and det A = -1. Then, following the Cappell-Shaneson construction, we consider the manifold Q (A), which is obtained from X by removing a tubular neighborhood of an embedded circle representing an orientation reversing element of $\pi\sb1$X and replacing it by a certain bundle over S$\sp1$ with fibre the compliment of an open cell in the 3-torus. By using the Seiberg-Witten theory we prove that if det (I-A$\sp2)=$ det (I-A$\sp6)$ then there exists an exotic smooth structure on Q (A) # CP$\sp2$ # $\rm\overline CP\sp2.$

Mathematics

#### Recommended Citation

Chkhenkeli, Mikhail, "Exotic smooth structures on 4-manifolds" (1996). Dissertations available from ProQuest. AAI9627901.
https://repository.upenn.edu/dissertations/AAI9627901

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