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: Research Article Estimating Nielsen Numbers on Wedge Product Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 83420 16 pages doi 2007 83420 Research Article Estimating Nielsen Numbers on Wedge Product Spaces Nirattaya Khamsemanan and Seung Won Kim Received 8 May 2007 Accepted 14 November 2007 Recommended by Evelyn Hart Let f X - X be a self-map of a finite polyhedron that is an aspherical wedge product space X. In this paper we estimate the Nielsen number N f of f. In particular we study some algebraic properties of the free products and then estimate Nielsen numbers on torus wedge surface with boundary Klein bottle wedge surface with boundary and torus wedge torus. Copyright 2007 N. Khamsemanan and S. W. Kim. 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 Let X be a space and let f X- X be a self-map. Let Fix f x e X f x x denote the fixed point set. The Nielsen number N f provides a lower bound for min Fix g g f and is often sharp. But in general it is very difficult to compute N f from its definition. For background on Nielsen fixed point theory see 1-3 . For a given space X algebraic properties of its fundamental group n1 X are usually important to compute Nielsen numbers on it. However if the fundamental group of X is free or a free product group then computing Nielsen number on X is extremely difficult see 4 . In this paper we estimate the Nielsen numbers on aspherical wedge product spaces focusing on the following three cases 1 torus wedge surface with boundary 2 Fixed Point Theory and Applications 2 Klein bottle wedge surface with boundary 3 torus wedge torus. It is well known that the fundamental group of the wedge product of spaces is the free product of the fundamental groups of the spaces. In Section 2 we present several properties of free product of groups which we use in the final .
