Mathematical Research Letters

Volume 20 (2013)

Number 2

Gluck twisting 4-manifolds with odd intersection form

Pages: 385 – 389



Selman Akbulut (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Kouichi Yasui (Department of Mathematics, Graduate School of Science, Hiroshima University, Hiroshima, Japan)


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.

Published 3 December 2013