tailieunhanh - Báo cáo hóa học: "ALGEBRAIC PERIODS OF SELF-MAPS OF A RATIONAL EXTERIOR SPACE OF RANK 2"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: ALGEBRAIC PERIODS OF SELF-MAPS OF A RATIONAL EXTERIOR SPACE OF RANK 2 | ALGEBRAIC PERIODS OF SELF-MAPS OF A RATIONAL EXTERIOR SPACE OF RANK 2 GRZEGORZ GRAFF Received 29 November 2004 Revised 27 January 2005 Accepted 21 July 2005 The paper presents a complete description of the set of algebraic periods for self-maps of a rational exterior space which has rank 2. Copyright 2006 Grzegorz Graff. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction A natural number m is called a minimal period of a map f if fm has a fixed point which is not fixed by any earlier iterates. One important device for studying minimal periods are the integers im f yk mp m k L fk where L fk denotes the Lefschetz number of fk and p is the classical Mobius 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 space M 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