Simplicial approach to derived differential manifolds
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 DOI:
 10.48550/arXiv.1112.0033
 arXiv:
 arXiv:1112.0033
 Bibcode:
 2011arXiv1112.0033B
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 23 pages