Mathematical Research Letters
Volume 20 (2013)
Gluck twisting 4-manifolds with odd intersection form
Pages: 385 – 389
We give a simple criterion when a Gluck twisting an odd smooth 4-manifold along a 2-sphere $S \subset X$ does not change its diffeomorphism type.We obtain this result by handlebody techniques and plug twisting operation, getting a slightly stronger version of the known fact that Gluck twisting of a 2-sphere $S \subset X$ of a compact smooth 4-manifold with an odd spherical class, in the complement of S, does not change the diffeomorphism type of $X$. This is the best possible result on Gluck twisting manifolds with odd homology classes.
4-manifold, smooth structure, Gluck twist
2010 Mathematics Subject Classification
Primary 57R55. Secondary 57R65.