Algebraic Periods of Self-maps of a Rationalexterior Space of Rank 2

A natural numberm is called a minimal period of a map f if f m has a fixed point which is not fixed by any earlier iterates. One important device for studying minimal periods are the integers im( f )= ∑ k/m μ(m/k)L( f k), where L( f k) denotes the Lefschetz number of f k and μ is the classical Möbius function. If im( f ) = 0, then we say that m is an algebraic period of f . In many cases the fact that m is an algebraic period provides information about the existence of minimal periods that are less then or equal to m. For example, let us consider f , a self-map of a compact manifold. If f is a transversal map and odd m is an algebraic period, then m is a minimal period (cf. [10, 12]). If f is a nonconstant holomorphic map, then there exists M > 0 such that for each prime number m >M, m is a minimal period of f if and only if m is an algebraic period of f (cf. [3]). Further relations between algebraic and minimal periods may be found in [8]. Sometimes the structure of the set of algebraic periods is a property of the space and may be deduced from the form of its homology groups. In [11] there is a description of algebraic periods for self-maps of a space M with three nonzero (reduced) homology groups, each of which is equal to Q, in [6] the authors consider a spaceM with nonzero homology groups H0(M;Q) =Q, H1(M;Q) =Q⊕Q. The main difficulty in giving the overall description in the latter case is that for a map f∗ induced by f on homology, for each m there are complex eigenvalues for which m is not an algebraic period. Rational exterior spaces are a wide class of spaces (e.g., Lie groups) which do not have this disadvantage, namely under the natural assumption of essentiality of f there is a constant mX and computable set TM , such that if m >mX , m ∈ TM , then m is an algebraic period of f (cf. [5]). The aim of this paper is to provide a full characterization of algebraic periods