Semifree actions of free groups
نویسنده
چکیده
We study countable universes similar to a free action of a group G. It turns out that this is equivalent to the study of free semi-actions of G, with two universes being transformable iff one corresponding free semi-action can be obtained from the other by a finite alteration. In the case of a free group G (in finitely many or countably many generators), a classification is given. Mathematics Subject Classification (2000) Primary 03C45 · Secondary 20F05
منابع مشابه
Semifree Actions of Finite Groups on Homotopy Spheres
We show that for any finite group the group of semifree actions on homotopy spheres of some fixed even dimension is finite, provided that the dimension of the fixed point set is greater than 2. The argument shows that for such an action the normal bundle to the fixed point set is equivariantly, stably trivial. 0. Introduction. A group G is said to act semifreely on a space X if every point is e...
متن کاملDifferentiable Actions on 2 « - Spheres
Introduction. It is shown in [4] that there is an infinite family of semifree Zm actions on odd dimensional homotopy spheres. There is also an infinite family of semifree S actions on odd dimensional homotopy spheres (see [2], [5]). On the other hand, it is announced in [2] that there are only finitely many inequivalent semifree S actions on even dimensional homotopy spheres. Hence it is intere...
متن کاملThe Atiyah-singer Invariant, Torsion Invariants, and Group Actions on Spheres
This paper deals with the classification of cyclic group actions on spheres using the Atiyah-Singer invariant and Reidemeister-type torsion. Our main tool is the computation of the group of relative homotopy triangulations of the product of a disk and a lens space. These results are applied to obtain lower bounds on the image of an equivariant /-homomorphism. Introduction. Smooth actions of fin...
متن کاملGeneralized Rochlin Invariants of Fixed Point Sets
The Rochlin invariant for 3-manifolds is extended to higher dimensions using a result of Ochanine. Given a semifree differentiable S-action on a closed mod 2 homology sphere M with fixed point set F , generalized Rochlin invariants are definable for both M and F , and one result of this paper states that these two invariants are equal. This yields restrictions on the types of semifree different...
متن کاملHomologically Trivial Group Actions on 4-Manifolds
In this paper we investigate pseudofree homologically trivial actions of arbitrary finite groups on simply connected 4-manifolds. It turns out that there are surprisingly strong restrictions on the groups and on the actions, especially when one considers the fact that any finite group can act, even freely, on some simply connected 4-manifold. Recall that a finite group action is free if no nont...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 46 شماره
صفحات -
تاریخ انتشار 2007