Abstract
In this paper we answer a question of Mike Freedman, regarding the efficiency of positive topological field theories as invariants of smooth manifolds in dimensions greater than 4. We show that simply connected closed 5-manifolds can be distinguished by such invariants. Using Barden’s classification, this follows from our result which says that homology groups and the vanishing of cohomology operations with finite coefficients are detected by positive topological field theories. Moreover, we prove that in the non-simply connected case, as well as in all dimensions d> 5, the universal manifold pairing (and in particular, d-dimensional positive topological field theories) are not sufficient to distinguish compact d-manifolds with boundary S 3 × S n , n> 1, and S 4 k −1 , k> 1. The latter case is equivalent to the same statement for closed 4k-manifolds.
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.
