Abstract
Given a simply connected, closed 4-manifold, we prove that the homotopy groups of such a manifold are determined by its second Betti number, and the ranks of the homotopy groups can be explicitly calculated. We show that for a generic metric on such a smooth 4-manifold with second Betti number at least three the number of geometrically distinct periodic geodesics of length at most l grows exponentially as a function of l.
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.
