The tangle hypothesis is a variant of the cobordism hypothesis that considers cobordisms embedded in some finite-dimensional Euclidean space (together with framings). Such tangles of codimension k can be organized into an E_k-monoidal d-category, where d is the maximal dimension of the tangles. The tangle hypothesis then asserts that this category of tangles is the free E_k-monoidal d-category with duals generated by a single object.<\/p>\n\n\n\n
In this talk, based on joint work in progress with Yonatan Harpaz, I will describe an\u00a0infinitesimal\u00a0version of the\u00a0tangle\u00a0hypothesis: Instead of showing that the E_k-monoidal category of\u00a0tangles\u00a0is freely generated by an object, we show that its cotangent complex is free of rank 1. This provides support for the\u00a0tangle\u00a0hypothesis\u00a0(of which it is a direct consequence), but can also be used to reduce the\u00a0tangle\u00a0hypothesis\u00a0to a statement at the level of E_k-monoidal (d+1, d)-categories by means of obstruction theory.
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Recording:<\/p>\n\n\n\n
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