Abstract
We study the relationship between exotic ’s and Stein surfaces as it applies to smoothing theory on more general open –manifolds. In particular, we construct the first known examples of large exotic ’s that embed in Stein surfaces. This relies on an extension of Casson’s embedding theorem for locating Casson handles in closed –manifolds. Under sufficiently nice conditions, we show that using these ’s as end-summands produces uncountably many diffeomorphism types while maintaining independent control over the genus-rank function and the Taylor invariant.
Citation
Julia Bennett. "Exotic smoothings via large $\mathbb{R}^4$'s in Stein surfaces." Algebr. Geom. Topol. 16 (3) 1637 - 1681, 2016. https://doi.org/10.2140/agt.2016.16.1637
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