2012/09/19 by Hugo Garcia-Compean, Hugo García‐Compeán, Garcia-Compean, Hugo +4
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1209.4155
34 pages, no figures
arxiv created 2012/09/19 · openalex publication_date 2012/09/19 · arxiv updated 2012/09/20 · openalex created_date 2022/10/17 · openalex updated_date 2026/07/28
The Jones-Witten invariants can be generalized for non-singular smooth vector fields with invariant probability measure on 3-manifolds, giving rise to new invariants of dynamical systems [22]. After a short survey of cohomological field theory for Yang-Mills fields, Donaldson-Witten invariants are generalized to four-dimensional manifolds with non-singular smooth flows generated by homologically non-trivial p-vector fields. These invariants have the information of the flows and they are interpreted as the intersection number of these flow orbits and constitute invariants of smooth four-manifolds admitting global flows. We study the case of Kahler manifolds by using the Witten's consideration of the strong coupling dynamics of N=1 supersymmetric Yang-Mills theories. The whole construction is performed by implementing the notion of higher dimensional asymptotic cycles a la Schwartzman [18]. In the process Seiberg-Witten invariants are also described within this context. Finally, we give an interpretation of our asymptotic observables of 4-manifolds in the context of string theory with flows.