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Transversal homotopy theory of Whitney stratified manifolds
We modify the theory of homotopy groups to obtain invariants of Whitney stratified spaces by considering smooth maps which are transversal to all strata, and smooth homotopies through such maps. Using this idea we obtain transversal homotopy monoids with duals for any Whitney stratified space. Just as in ordinary homotopy theory we may also define higher categorical invariants of spaces. Here instead of groupoids we obtain categories with duals. We concentrate on examples involving the sphere,doi:10.17638/00006653 fatcat:vm57guse4ndtvhy5jjmzcrmcxe