Jump to ContentJump to Main Navigation
Frontiers in Complex DynamicsIn Celebration of John Milnor's 80th Birthday$
Users without a subscription are not able to see the full content.

Araceli Bonifant, Misha Lyubich, and Scott Sutherland

Print publication date: 2014

Print ISBN-13: 9780691159294

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691159294.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 22 September 2021

Invariants of four-manifolds with flows via cohomological field theory

Invariants of four-manifolds with flows via cohomological field theory

(p.645) Invariants of four-manifolds with flows via cohomological field theory
Frontiers in Complex Dynamics

Hugo Garcia-Compeân

Roberto Santos-Silva

Alberto Verjovsky

, Araceli Bonifant, Mikhail Lyubich, Scott Sutherland
Princeton University Press

This chapter argues that the Jones–Witten invariants can be generalized for smooth, nonsingular vector fields with invariant probability measure on three-manifolds, thus giving rise to new invariants of dynamical systems. 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. The chapter studies the case of Kähler 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. In the process Seiberg–Witten invariants are also described within this context. Finally, the chapter gives an interpretation of the asymptotic observables of four-manifolds in the context of string theory with flows.

Keywords:   Jones–Witten invariants, cohomological field theory, dynamical systems, Yang–Mills fields, Donaldson–Witten invariants, four-dimensional manifolds, Kähler manifolds, higher-dimensional asymptotic cycles, Seiberg–Witten invariants

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.