Journal of Differential Geometry

Cork twisting exotic Stein 4-manifolds

Selman Akbulut and Kouichi Yasui

Full-text: Open access

Abstract

From any 4-dimensional oriented handlebody $X$ without 3- and 4-handles and with $b_2 \ge 1$, we construct arbitrary many compact Stein 4-manifolds that are mutually homeomorphic but not diffeomorphic to each other, so that their topological invariants (their fundamental groups, homology groups, boundary homology groups, and intersection forms) coincide with those of $X$. We also discuss the induced contact structures on their boundaries. Furthermore, for any smooth 4-manifold pair $(Z, Y)$ such that the complement $Z − \operatorname{int} Y$ is a handlebody without 3- and 4-handles and with $b_2 \ge 1$, we construct arbitrary many exotic embeddings of a compact 4-manifold $Y'$ into $Z$, such that $Y'$ has the same topological invariants as $Y$.

Article information

Source
J. Differential Geom., Volume 93, Number 1 (2013), 1-36.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1357141505

Digital Object Identifier
doi:10.4310/jdg/1357141505

Mathematical Reviews number (MathSciNet)
MR3019510

Zentralblatt MATH identifier
1280.57030

Citation

Akbulut, Selman; Yasui, Kouichi. Cork twisting exotic Stein 4-manifolds. J. Differential Geom. 93 (2013), no. 1, 1--36. doi:10.4310/jdg/1357141505. https://projecteuclid.org/euclid.jdg/1357141505


Export citation