Western University Scholarship@Western Electronic Thesis and Dissertation Repository 6-25-2015 12:00 AM Algorithms to Compute Characteristic Classes Martin Helmer The University of Western Ontario Supervisor Eric Schost The University of Western Ontario Graduate Program in Applied Mathematics A thesis submitted in partial fulfillment of the equirr ements for the degree in Doctor of Philosophy © Martin Helmer 2015 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Algebra Commons, Algebraic Geometry Commons, Geometry and Topology Commons, Other Applied Mathematics Commons, and the Theory and Algorithms Commons Recommended Citation Helmer, Martin, "Algorithms to Compute Characteristic Classes" (2015). Electronic Thesis and Dissertation Repository. 2923. https://ir.lib.uwo.ca/etd/2923 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact
[email protected]. Algorithms to Compute Characteristic Classes (Thesis Format: Integrated-Article) by Martin Helmer Graduate Program in Applied Mathematics A thesis submitted in partial fulfilment of the requirements for a Doctor of Philosophy The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada c Martin Helmer 2015 i Abstract In this thesis we develop several new algorithms to compute characteristic classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (cSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).