Constructing free actions ofp–groups on products of spheres

Constructing homologically trivial actions on products of spheres

“…As a corollary of Proposition 4.1, we obtain the following which is also proved in [12] as Proposition 2.7. 7, [12]).…”

“…In different forms, this proposition also appears in [4], [12], and [18]. Here we give a proof of it for completeness since it is the main ingredient in the proof of Theorem 1.2.…”

“…The main purpose of this section is to prove the following theorem which is due to M. Klaus [12]. We give a different proof here using the equivariant Federer spectral sequence which was introduced by Møller in [14].…”

“…For more details on this material we refer the reader to [13] and [22]. Some of this material also appears in [4], [9], [12], and [18]. Definition 2.1.…”

“…Every finite group acts freely and homologically trivially on some finite CW-complex X homotopy equivalent to a product of spheres The paper is organized as follows: In Section 2, we introduce G-fibrations and discuss the effects of taking fiber joins of G-fibrations. In Section 3, we discuss the equivariant Federer spectral sequence introduced by Møller [14] and using it, we give another proof for a theorem by M. Klaus [12] (see Theorem 3.1). In Section 4, we introduce our main construction method, and finally in Section 5, we prove Theorem 1.2.…”