OrlikSolomon

OrlikSolomon is a mathematical object that is a fundamental example in the study of 3-manifolds and knot theory. It is named after its discoverers, David Orlik and Robert Solomon, who introduced it in their 1980 paper "A complete set of invariants for knots and 3-manifolds." The OrlikSolomon space is a 3-manifold that is constructed by taking the product of a circle with a 2-dimensional space that is the complement of a certain graph in the plane. This graph is known as the OrlikSolomon graph, and it has a specific structure that makes the resulting 3-manifold interesting from a topological perspective. The OrlikSolomon space is an example of a Seifert fiber space, which is a type of 3-manifold that has a specific fibering structure. It is also an example of a graph manifold, which is a 3-manifold that is constructed by gluing together solid tori along their boundaries in a specific way. The OrlikSolomon space has been studied extensively in the context of 3-manifold topology, and it has been used as a tool for understanding the structure of more general 3-manifolds. It is also an important example in the study of knot theory, as it can be used to construct examples of knots and links with specific properties.