Constructing Homologically Trivial Actions on Products of Spheres
نویسنده
چکیده
We prove that if a finite group G has a representation with fixity f , then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of f + 1 spheres. This shows, in particular, that every finite group acts freely and homologically trivially on some finite CW-complex homotopy equivalent to a product of spheres.
منابع مشابه
Any Finite Group Acts Freely and Homologically Trivially on a Product of Spheres
The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...
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