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Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”, Preprint arXiv:0809.0086
"... We define the twisted de Rham cohomology and show how to use it to define the notion of an integral of the form ∫ g(x)e f(x) dx over an arbitrary ring. We discuss also a definition of a family of integrals and some properties of the homological definition of integral. We show how to use the twisted ..."
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We define the twisted de Rham cohomology and show how to use it to define the notion of an integral of the form ∫ g(x)e f(x) dx over an arbitrary ring. We discuss also a definition of a family of integrals and some properties of the homological definition of integral. We show how to use the twisted de Rham cohomology in order to define the Frobenius map on the padic cohomology. Finally, we consider twodimensional topological quantum field theories with general coefficients. 1
Supermanifolds from Feynman graphs
 Journal of Physics A
"... Abstract. We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integ ..."
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Abstract. We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying a condition generalizing the log divergence in this context. The analog in this setting of the graph hypersurfaces is a graph supermanifold given by the divisor of zeros and poles of the Berezinian of a matrix associated to the graph, inside a superprojective space. We introduce a Grothendieck group for supermanifolds and we identify the subgroup generated by the graph supermanifolds. This can be seen as a general procedure to construct interesting classes of supermanifolds with associated periods.
padic superspaces and Frobenius.
, 2006
"... The notion of a padic superspace is introduced and used to give a transparent construction of the Frobenius map on padic cohomology of a smooth projective variety over Zp (the ring of padic integers). This is a companion article to [7] containing the omitted proofs as well as providing a more mat ..."
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Cited by 1 (0 self)
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The notion of a padic superspace is introduced and used to give a transparent construction of the Frobenius map on padic cohomology of a smooth projective variety over Zp (the ring of padic integers). This is a companion article to [7] containing the omitted proofs as well as providing a more mathematical point of view. 1
On the Divided Power Structures in Super Rings by
, 2014
"... This online database contains the fulltext of PhD dissertations and Masters ’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license— ..."
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This online database contains the fulltext of PhD dissertations and Masters ’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license—CC BYNCND (Attribution, NonCommercial, No Derivative Works). Under this license, works must always be attributed to the copyright holder (original author), cannot be used for any commercial purposes, and may not be altered. Any other use would require the permission of the copyright holder. Students may inquire about withdrawing their dissertation and/or thesis from this database. For additional inquiries, please contact the repository administrator via email (scholarship@uwindsor.ca) or by telephone at 5192533000ext. 3208.