The researcher has systematically explored several key areas within advanced algebraic topology, including the classification of Hopf invariant one elements in 2015. Building on this foundation, they extended these concepts to cobordism categories with group actions in 2017. Their work also delved into topological cyclic homology in 2018, and further contributions were made to equivariant stable homotopy theory in 2019. Additionally, the researcher examined the intersection of topology with category theory through higher categorical structures in 2020, thereby creating a comprehensive framework that links various mathematical domains while building upon earlier insights.
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