Abstract
Let be a finite polyhedron that has the homotopy type of the wedge of the projective plane and the circle. With the aid of techniques from combinatorial group theory, we obtain formulas for the Nielsen numbers of the selfmaps of .
Highlights
Compact surfaces were the setting of Nielsen’s fixed point theory in 1927 1, until relatively recently the calculation of the Nielsen number was restricted to maps of very few surfaces
It applies to many maps and recent research has significantly extended the class of such maps whose Nielsen number can be calculated see 4–7 and, especially, the survey article 8
The purpose of this paper is to demonstrate that combinatorial group theory furnishes powerful tools for the calculation of Nielsen numbers, even for maps of a nonaspherical space
Summary
Compact surfaces were the setting of Nielsen’s fixed point theory in 1927 1 , until relatively recently the calculation of the Nielsen number was restricted to maps of very few surfaces. It applies to many maps and recent research has significantly extended the class of such maps whose Nielsen number can be calculated see 4–7 and, especially, the survey article 8 This approach makes use of the fact that a surface with boundary has the homotopy type of a wedge of circles. The key properties of surfaces with boundary that are exploited in the Wagner-type calculations are that they have the homotopy type of a wedge and that they are aspherical spaces so their selfmaps are classified up to homotopy by the induced homomorphisms of the fundamental group. The purpose of this paper is to demonstrate that combinatorial group theory furnishes powerful tools for the calculation of Nielsen numbers, even for maps of a nonaspherical space.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
