Morse-Floer Theory for Super-quadratic Dirac-Geodesics
Takeshi Isobe, Ali Maalaoui
TL;DR
This paper develops a Morse-Floer homology for super-quadratic Dirac-geodesics, providing explicit computations and new existence results for these geometric objects.
Contribution
It introduces a novel Morse-Floer homology framework for super-quadratic Dirac-geodesics and computes it explicitly using spectral sequences.
Findings
Explicit Morse-Floer homology computation for Dirac-geodesics
New existence results for Dirac-geodesics
Application of spectral sequences in geometric analysis
Abstract
In this paper we present the full details of the construction of a Morse-Floer type homology related to the super-quadratic perturbation of the Dirac-geodesic model. This homology is computed explicitly using a Leray-Serre type spectral sequence and this computation leads us to several existence results of Dirac-geodesics.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows