A genus- handlebody is a three-ball with one-handles attached. Its boundary is a closed orientable topological surface of genus .
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A handlebody is a specific type of topological space that is often studied in the field of algebraic topology. More formally, a handlebody of genus \( g \) is defined as a quotient of a disjoint union of \( g \) solid tori by identifying their boundaries in a certain way.