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2016 Exotic smoothings via large $\mathbb{R}^4$'s in Stein surfaces
Julia Bennett
Algebr. Geom. Topol. 16(3): 1637-1681 (2016). DOI: 10.2140/agt.2016.16.1637

Abstract

We study the relationship between exotic 4’s and Stein surfaces as it applies to smoothing theory on more general open 4–manifolds. In particular, we construct the first known examples of large exotic 4’s that embed in Stein surfaces. This relies on an extension of Casson’s embedding theorem for locating Casson handles in closed 4–manifolds. Under sufficiently nice conditions, we show that using these 4’s as end-summands produces uncountably many diffeomorphism types while maintaining independent control over the genus-rank function and the Taylor invariant.

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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

Information

Received: 25 November 2014; Revised: 20 September 2015; Accepted: 29 September 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1350.57026
MathSciNet: MR3523051
Digital Object Identifier: 10.2140/agt.2016.16.1637

Subjects:
Primary: 57N13
Secondary: 57R55

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 3 • 2016
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