Inventor: Sleator & Tarjan.
Used to maintain dynamic forests and to handle path related queries. It can also manage subtree information to some degree.
Under the hood, LCT uses splay tree to manage its structure. After some time complexity analysis, you get for link, cut operations.
Related
Heavy-light decomposition
Top Tree: swiss army knife version of a link-cut tree, capable of handling heavy-duty subtree augmentation.
Applications
Speeding up Dinitz’s algorithm with Link-cut tree