Cyclic Group Actions on Contractible 4-manifolds Nima Anvari and Ian Hambleton
نویسندگان
چکیده
There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that smooth free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which the actions extend locally linearly but not smoothly.
منابع مشابه
A Four-manifold Approach to the Spherical Space Form Problem
For certain 3-manifolds M with finite fundamental group, we construct smooth, negative definite 4-manifolds, with boundary containingM and some orthogonal spherical spaces forms. This allows a translation of the existence problem for finite fundamental groups of 3-manifolds into a problem in equivariant gauge theory.
متن کاملNon-smoothable Four-manifolds with Infinite Cyclic Fundamental Group
In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group Z that does not split off S1 × S3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain topologically slice knots that are not smoot...
متن کاملOn Certain 5-manifolds with Fundamental Group of Order 2
In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.
متن کاملTopological 4-manifolds with Geometrically 2-dimensional Fundamental Groups
Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w2-type, equivariant intersection form and the Kirby-Siebenmann invariant. As an application, we obtain a complete homeomorphism classification of closed oriented 4-manifolds with solvable Baumslag-Solitar fundamental groups, including...
متن کاملConjugation Spaces and 4-manifolds
We show that 4-dimensional conjugation manifolds are all obtained from branched 2-fold coverings of knotted surfaces in Z2-homology 4-spheres.
متن کامل