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Dec 9, 2021 at 23:05 comment added Igor Belegradek Usually, characteristic classes are invariants of (vector or principal) bundles, not manifolds, e.g. Stiefel-Whitney classes of a manifold depend on its tangent bundle. One can also define the Stiefel-Whitney classes in the topological case for the tangent microbundle, see e.g. mathoverflow.net/questions/243629/…. What bundle are you considering over your simplicial complex? What is a wish list (a set of properties) for the invariant you are trying to define?
Dec 9, 2021 at 22:40 history edited wonderich CC BY-SA 4.0
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Dec 9, 2021 at 18:25 comment added wonderich One ref I know is Alexander_A_Gaifullin_2005_Russ._Math._Surv._60_615_Computation of characteristic classes of a manifold from a triangulation of it maths.ed.ac.uk/~v1ranick/papers/gaifullin.pdf, but there also is a manifold, with some triangulations
Dec 9, 2021 at 18:14 comment added Tim Campion Is there some reference where I can read about branching structures? I'm confused by your description, because so far as I can see there is no reason for the link of a vertex to be a manifold, and so I don't know what it means to choose an orientation of the link.
Dec 9, 2021 at 18:12 comment added Tim Campion Cross-posted
Dec 9, 2021 at 17:33 history asked wonderich CC BY-SA 4.0