Simplicial approach to derived differential manifolds

Details Simplicial approach to derived differential manifolds Simplicial approach to derived differential manifolds

2011-11-30

arxiv.org/abs/1112.0033v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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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