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Explore the intricacies of virtual manifolds and their complexity in this comprehensive lecture by E. Fominykh. Delve into advanced concepts of quantum topology as the speaker presents a detailed analysis of virtual manifolds, their properties, and the challenges associated with understanding their complexity. Gain insights into cutting-edge research in this field and discover how these mathematical structures contribute to our understanding of quantum systems and topological spaces. Enhance your knowledge of advanced mathematics and theoretical physics through this in-depth presentation, suitable for graduate students and researchers in related fields.