The Use of Dual B-Spline Representations for the Double de Rham Complex of Discrete Differential Forms

2020 ◽  
pp. 227-242
Author(s):  
Yi Zhang ◽  
Varun Jain ◽  
Artur Palha ◽  
Marc Gerritsma
Keyword(s):  
Differential Forms ◽  
B Spline ◽  
De Rham Complex ◽  
Discrete Differential Forms ◽  
Rham Complex ◽  
De Rham

scholarly journals Novikov type inequalities for differential forms with non-isolated zeros

1997 ◽  
Vol 122 (2) ◽  
pp. 357-375 ◽  
Author(s):  
MAXIM BRAVERMAN ◽  
MICHAEL FARBER
Keyword(s):  
Critical Points ◽  
Differential Forms ◽  
Explicit Estimate ◽  
Morse Inequalities ◽  
De Rham Complex ◽  
Analytic Proof ◽  
Rham Complex ◽  
De Rham ◽  
Flat Bundle ◽  
Witten Deformation

We generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R. Bott) and, secondly, we strengthen the inequalities by means of twisting by an arbitrary flat bundle. The proof uses Bismut's modification of the Witten deformation of the de Rham complex; it is based on an explicit estimate on the lower part of the spectrum of the corresponding Laplacian.In particular, we obtain a new analytic proof of the degenerate Morse inequalities of Bott.

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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