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Free keywords:
Mathematics, Geometric Topology
Abstract:
We show that every smooth, orientable, closed, connected 4-manifold can be
represented by a loop in the pants complex. We use this representation,
together with the fact that the pants complex is simply connected, to provide
an elementary proof that such 4-manifolds are smoothly cobordant to $\coprod_m
\mathbb{C}P^2 \coprod_n \bar{\mathbb{C}P}^2$. We also use this association to
give information about the structure of the pants complex. Namely, given a loop
in the pants complex, $L$, which bounds a disk, $D$, we show that the signature
of the 4-manifold associated to $L$ gives a lower bound on the number of
triangles in $D$.
