scholarly journals A Perturbation of the de Rham Complex

2020 ◽  
pp. 519-532
Author(s):  
Ihsane Malass ◽  
Nikolai Tarkhanov
Keyword(s):  
Euler Characteristic ◽  
Compact Manifold ◽  
Cohomology Theory ◽  
The Other ◽  
De Rham Complex ◽  
Manifold With Boundary ◽  
Other Hand ◽  
Rham Complex ◽  
De Rham ◽  
Natural Way

We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

scholarly journals Chiral de Rham Complex over Locally Complete Intersections

2015 ◽  
Vol 15 (2) ◽  
pp. 353-372
Author(s):  
Fyodor Malikov ◽  
Vadim Schechtman
Keyword(s):  
Complete Intersections ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham

scholarly journals Duality symmetry of the p-form effective action and supertrace of the twisted de Rham complex

2003 ◽  
Vol 648 (3) ◽  
pp. 542-556 ◽  
Author(s):  
P. Gilkey ◽  
K. Kirsten ◽  
D. Vassilevich ◽  
A. Zelnikov
Keyword(s):  
Effective Action ◽  
De Rham Complex ◽  
Duality Symmetry ◽  
Rham Complex ◽  
De Rham

scholarly journals A discrete de Rham complex with enhanced smoothness

CALCOLO ◽  
2006 ◽  
Vol 43 (4) ◽  
pp. 287-306 ◽  
Author(s):  
Xue–Cheng Tai ◽  
Ragnar Winther
Keyword(s):  
De Rham Complex ◽  
Rham Complex ◽  
De Rham
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