Deforming homotopy involutions of 3-manifolds to involutions

Free Involutions on Homotopy (4&+3)-spheres

In [ l ] Browder and Livesay defined an invariant a(Tt 2 ) £ 8 Z of a free differentiate involution T of a homotopy (4&+3)-sphere 2 , k>0. I t is the precise obstruction to finding an invariant (4&+2)sphere of the involution. In [5] and [ô] Medrano showed how to construct free involutions with arbitrary Browder-Livesay invariant on some homotopy (4&+3) -spheres and hence that there exist infini...

Involutions on Spin 4-manifolds

We show that a simply-connected spin 4-manifold which admits a locally linear involution must have vanishing signature. We also show that the codimensions of all components of the fixed point set of an involution on a spin 4-manifold are the same modulo 4 . There is no assumption of local linearity in this result, which extends a lemma of Atiyah and Bott. This note records two results about inv...

Surgery and involutions on 4-manifolds

We prove that the canonical 4-dimensional surgery problems can be solved after passing to a double cover. This contrasts the longstanding conjecture about the validity of the topological surgery theorem for arbitrary fundamental groups (without passing to a cover). As a corollary, the surgery conjecture is reformulated in terms of the existence of free involutions on a certain class of 4-manifo...

Involutions of 3-dimensional Handlebodies

We study the orientation preserving involutions of the orientable 3-dimensional handlebody Hg, for any genus g. A complete classification of such involutions is given in terms of their fixed points.

On Involutions of the 3-Sphere