A pair of pants is a compact surface obtained from a sphere by removing the interiors of three pairwise disjoint closed disks. Equivalently, it is a closed disk with the interiors of two pairwise disjoint closed disks removed (Farb and Margalit 2012, p. 53). It is an orientable surface of genus 0 with three boundary components, and its Euler characteristic is
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Pairs of pants are building blocks for compact orientable surfaces with negative Euler characteristic. A pants decomposition is obtained by cutting such a surface along pairwise disjoint simple closed curves so that every resulting component is a pair of pants (Buser 1992).
