No Access
Finite order corks
Abstract
We show that for any positive integer , there exist pairs of compact, contractible, Stein 4-manifolds and order self-diffeomorphisms of the boundaries that do not extend to the full manifolds. Each boundary of the Stein 4-manifolds is a cyclic branched cover along a slice knot embedded in the boundary of a contractible 4-manifold. Each pair is called a finite order cork, we give a method producing examples of many finite order corks, which are possibly not a Stein manifold. The example of the Stein cork gives a diffeomorphism generating homotopic but non-isotopic Stein fillable contact structures for an arbitrary positive integer .
AMSC: 57R55, 57R65
References
- 1. , A fake compact contractible 4-manifold, J. Differential Geom. 33 (1991) 335–356. Crossref, ISI, Google Scholar
- 2. , Action of the cork twist on Floer homology, in Proc. Gökova Geometry-Topology Conf. 2011 (International Press, Somerville, MA, 2012), pp. 42–52. Google Scholar
- 3. , Exotic structures and adjunction inequality, Turkish J. Math. 21 (1997) 47–53. ISI, Google Scholar
- 4. , A convex decomposition theorem for 4-manifolds, Int. Math. Res. Not. 7 (1998) 371–381. Crossref, Google Scholar
- 5. , Lefschetz fibrations on compact Stein surfaces, Geom. Topol. 5 (2001) 319–334. Crossref, ISI, Google Scholar
- 6. , Equivariant corks, to appear in Algebr. Geom. Topol. 17(2) (2017), arXiv:1602.07650. Google Scholar
- 7. , A decomposition theorem for h-cobordant smooth simply-connected compact 4-manifolds, Invent. Math. 123(2) (1996) 343–348. Crossref, ISI, Google Scholar
- 8. , The topology of four-dimensional manifolds, J. Differential Geom. 17(3) (1982) 357–453. Crossref, ISI, Google Scholar
- 9. , Handlebody construction of Stein surfaces, Ann. Math. 148(2) (1998) 619–693. Crossref, ISI, Google Scholar
- 10. , Infinite order corks, to appear in Geom. Topol. 21(2) (2017), arXiv:1603.05090. Google Scholar
- 11. , 4-Manifolds and Kirby Calculus,
Graduate Studies in Mathematics , Vol. 20 (American Mathematical Society, Providence, RI, 1999). Crossref, Google Scholar - 12. , A decomposition of smooth simply-connected h-cobordant 4-manifolds, J. Differential Geom. 44(3) (1996) 571–582. Crossref, ISI, Google Scholar
- 13. , Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202(2) (2006) 326–400. Crossref, ISI, Google Scholar
- 14. , Contact structures with distinct Heegaard Floer invariants, Math. Res. Lett. 11 (2004) 547–561. Crossref, ISI, Google Scholar
- 15. , A plug with infinite order and some exotic structures, J. GGT 9 (2015) 1–17. ISI, Google Scholar
Published: 30 May 2017
| Remember to check out the Most Cited Articles in IJM ! |
Check out our NEW Mathematics books for inspirations & up-to-date information in your research area!
