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arxiv: 1112.0033 · v1 · pith:IV2RD2UBnew · submitted 2011-11-30 · 🧮 math.DG

Simplicial approach to derived differential manifolds

Dennis Borisov , Justin Noel This is my paper
classification 🧮 math.DG
keywords homotopyderiveddifferentialmanifoldsconstructedringssimplicialtheory
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Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This reduction to the usual algebraic homotopy can potentially lead to virtual fundamental classes beyond obstruction theory.

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    Proves a derived symplectic reduction theorem by modeling the quotient as a dg-groupoid and constructing a non-degenerate reduced form in the Bott-Shulman complex.