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A DoldKantype correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry
http://sms.cam.ac.uk/media/1454695
Roytenberg, D (Universiteit Utrecht)
Tuesday 02 April 2013, 15:0016:00
40
A DoldKantype correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry
http://sms.cam.ac.uk/media/1454695
http://rss.sms.cam.ac.uk/itunesimage/1393655.jpg
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A DoldKantype correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry
ucs_sms_1387512_1454695
http://sms.cam.ac.uk/media/1454695
A DoldKantype correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry
Roytenberg, D (Universiteit Utrecht)
Tuesday 02 April 2013, 15:0016:00
Mon, 08 Apr 2013 10:46:05 +0100
Isaac Newton Institute
Roytenberg, D
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Roytenberg, D (Universiteit Utrecht)
Tuesday 02 April 2013, 15:0016:00
Roytenberg, D (Universiteit Utrecht)
Tuesday 02 April 2013, 15:0016:00
Cambridge University
4080
http://sms.cam.ac.uk/media/1454695
A DoldKantype correspondence for superalgebras of differentiable functions and a "differential graded" approach to derived differential geometry
Roytenberg, D (Universiteit Utrecht)
Tuesday 02 April 2013, 15:0016:00
The commutative algebra appropriate for differential geometry is provided by the algebraic theory of C∞algebras  an enhancement of the theory of commutative algebras which admits all C∞ functions of n variables (rather than just the polynomials) as its nary operations. Derived differential geometry requires a homotopy version of these algebras for its underlying commutative algebra. We present a model for the latter based on the notion of a "differential graded structure" on a superalgebra of differentiable functions, understood  following Severa  as a (co)action of the monoid of endomorphisms of the odd line. This view of a differential graded structure enables us to construct, in a conceptually transparent way, a DoldKantype correspondence relating our approach with models based on simplicial C∞algebras, generalizing a classical result of Quillen for commutative and Lie algebras. It may also shed new light on DoldKantype co rrespondences in other contexts (e.g. operads and algebras over them). A similar differential graded approach exists for every geometry whose ground ring contains the rationals, such as real analytic or holomorphic.
This talk is partly based on joint work with David Carchedi (arXiv:1211.6134 and arXiv:1212.3745).
20130408T10:46:27+01:00
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