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arXiv · 2311.16322

Interaction homotopy and interaction homology

Jian Liu·Dong Chen·Guo-Wei Wei
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Abstract

Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces. In this work, we present an algebraic topology framework to explore interactions between spaces. We introduce the concept of interaction spaces and investigate their homotopy, singular homology, and simplicial homology. Furthermore, we demonstrate that interaction singular homology serves as an invariant under interaction homotopy. We believe that the proposed framework holds potential for practical applications.

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Jian Liu, Dong Chen, Guo-Wei Wei. 2023-11-27. Interaction homotopy and interaction homology. https://arxiv.org/abs/2311.16322

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