Hodge Conjecture

This study investigates the Hodge Conjecture through a geometric and structural analysis of algebraic cycles, differential forms, and complex manifold topology. The framework focuses on the relationship between Hodge classes and algebraic varieties, examining whether specific cohomology classes can be represented through algebraic-cycle structures under higher-dimensional geometric constraints. By combining concepts from algebraic geometry, topology, symmetry analysis, and multidimensional mathematical structures, the work explores how hidden geometric organization may emerge within complex projective spaces. The study also considers potential links between harmonic structures, dimensional transformations, and cohomological stability, aiming to construct an original conceptual framework for understanding the compatibility between algebraic and topological representations in complex manifolds.

Originality and AI-use statement:
This work is an original research output by Begüm Yıldırım. AI tools, if used, were limited to language refinement, grammar correction, formatting, translation assistance, and clarity improvement. The conceptual framework, research direction, interpretation, models, and conclusions belong to the author. External sources, datasets, or prior works are cited where applicable.