English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We demonstrate new applications of the trace embedding lemma to the study ofpiecewise-linear surfaces and the detection of exotic phenomena in dimensionfour. We provide infinitely many pairs of homeomorphic 4-manifolds $W$ and $W'$homotopy equivalent to $S^2$ which have smooth structures distinguished byseveral formal properties: $W'$ is diffeomorphic to a knot trace but $W$ isnot, $W'$ contains $S^2$ as a smooth spine but $W$ does not even contain $S^2$as a piecewise-linear spine, $W'$ is geometrically simply connected but $W$ isnot, and $W'$ does not admit a Stein structure but $W$ does. In particular, thesimple spineless 4-manifolds $W$ provide an alternative to Levine and Lidman'srecent solution to Problem 4.25 in Kirby's list. We also show that all smooth4-manifolds contain topological locally flat surfaces that cannot beapproximated by piecewise-linear surfaces.

The trace embedding lemma and spinelessness