Liftings of forms to Weil bundles and the exterior derivative

Jacek Dębecki

Annales Polonici Mathematici (2009)

  • Volume: 95, Issue: 3, page 289-300
  • ISSN: 0066-2216

Abstract

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In a previous paper we have given a complete description of linear liftings of p-forms on n-dimensional manifolds M to q-forms on T A M , where T A is a Weil functor, for all non-negative integers n, p and q, except the case p = n and q = 0. We now establish formulas connecting such liftings and the exterior derivative of forms. These formulas contain a boundary operator, which enables us to define a homology of the Weil algebra A. We next study the case p = n and q = 0 under the condition that A is acyclic. Finally, we compute the kernels and the images of the boundary operators for the Weil algebras k r and show that these algebras are acyclic.

How to cite

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Jacek Dębecki. "Liftings of forms to Weil bundles and the exterior derivative." Annales Polonici Mathematici 95.3 (2009): 289-300. <http://eudml.org/doc/280964>.

@article{JacekDębecki2009,
abstract = {In a previous paper we have given a complete description of linear liftings of p-forms on n-dimensional manifolds M to q-forms on $T^AM$, where $T^A$ is a Weil functor, for all non-negative integers n, p and q, except the case p = n and q = 0. We now establish formulas connecting such liftings and the exterior derivative of forms. These formulas contain a boundary operator, which enables us to define a homology of the Weil algebra A. We next study the case p = n and q = 0 under the condition that A is acyclic. Finally, we compute the kernels and the images of the boundary operators for the Weil algebras $^r_k$ and show that these algebras are acyclic.},
author = {Jacek Dębecki},
journal = {Annales Polonici Mathematici},
keywords = {natural operator Weil bundle},
language = {eng},
number = {3},
pages = {289-300},
title = {Liftings of forms to Weil bundles and the exterior derivative},
url = {http://eudml.org/doc/280964},
volume = {95},
year = {2009},
}

TY - JOUR
AU - Jacek Dębecki
TI - Liftings of forms to Weil bundles and the exterior derivative
JO - Annales Polonici Mathematici
PY - 2009
VL - 95
IS - 3
SP - 289
EP - 300
AB - In a previous paper we have given a complete description of linear liftings of p-forms on n-dimensional manifolds M to q-forms on $T^AM$, where $T^A$ is a Weil functor, for all non-negative integers n, p and q, except the case p = n and q = 0. We now establish formulas connecting such liftings and the exterior derivative of forms. These formulas contain a boundary operator, which enables us to define a homology of the Weil algebra A. We next study the case p = n and q = 0 under the condition that A is acyclic. Finally, we compute the kernels and the images of the boundary operators for the Weil algebras $^r_k$ and show that these algebras are acyclic.
LA - eng
KW - natural operator Weil bundle
UR - http://eudml.org/doc/280964
ER -

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