TL;DR
This paper introduces Lebesgue currents, a new mathematical concept involving Lebesgue measure, to define intersections of singular cycles, laying the groundwork for real intersection theory.
Contribution
It presents the concept of Lebesgue currents and applies them to establish a foundation for real intersection theory of singular cycles.
Findings
Definition of Lebesgue currents involving Lebesgue measure
Application to intersection of singular cycles
Foundation for real intersection theory
Abstract
We introduce the notion of Lebesgue currents. They are a special type of currents involving Lebesgue measure. We apply it to define the intersection of singular cycles, which provides the foundation to the real intersection theory.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Analytic Number Theory Research · Stochastic processes and financial applications