Nonsmoothable group actions on elliptic surfaces

Nonsmoothable Group Actions on Elliptic Surfaces

Let G be a cyclic group of order 3, 5 or 7, and X = E(n) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under certain conditions on n, there exists a locally linear G-action on X which is nonsmoothable with respect to infinitely many smooth structures on X . This extends the main result of [18].

Distortion Elements in Group actions on surfaces

If G is a finitely generated group with generators {g1, . . . , gj} then an infinite order element f ∈ G is a distortion element of G provided lim inf n→∞ |f|/n = 0, where |f| is the word length of f in the generators. Let S be a closed orientable surface and let Diff(S)0 denote the identity component of the group of C diffeomorphisms of S. Our main result shows that if S has genus at least two...

Area preserving group actions on surfaces

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional Heisenberg group. For example any finite index subgroup of SL(3, Z) is such a group. The main result of this paper is that every action of G on a closed oriented surface by area preserving diffeomorphisms factors through a finite group.

Acyclic curves and group actions on affine toric surfaces

We show that every irreducible, simply connected curve on a toric affine surface X over C is an orbit closure of a Gm-action on X . It follows that up to the action of the automorphism group Aut(X) there are only finitely many non-equivalent embeddings of the affine line A in X . A similar description is given for simply connected curves in the quotients of the affine plane by small finite line...

Group Actions on Graphs, Maps and Surfaces with Maximum Symmetry