The natural operators $T^{(0,0)}⇝T^{(1,1)}{T}^{\left(r\right)}$

Włodzimierz M. Mikulski. "The natural operators $T^{(0,0)} ⇝ T^{(1,1)}T^{(r)}$." Colloquium Mathematicae 96.1 (2003): 5-16. <http://eudml.org/doc/285093>.

@article{WłodzimierzM2003,
abstract = {We study the problem of how a map f:M → ℝ on an n-manifold M induces canonically an affinor $A(f): TT^\{(r)\}M → TT^\{(r)\}M$ on the vector r-tangent bundle $T^\{(r)\}M = (J^r(M,ℝ)₀)*$ over M. This problem is reflected in the concept of natural operators $A:T^\{(0,0)\}_\{|ℳ fₙ\} ⇝ T^\{(1,1)\}T^\{(r)\}$. For integers r ≥ 1 and n ≥ 2 we prove that the space of all such operators is a free (r+1)²-dimensional module over $^\{∞\}(T^\{(r)\}ℝ)$ and we construct explicitly a basis of this module.},
author = {Włodzimierz M. Mikulski},
journal = {Colloquium Mathematicae},
keywords = {bundle functors; natural transformations; natural operators},
language = {eng},
number = {1},
pages = {5-16},
title = {The natural operators $T^\{(0,0)\} ⇝ T^\{(1,1)\}T^\{(r)\}$},
url = {http://eudml.org/doc/285093},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Włodzimierz M. Mikulski
TI - The natural operators $T^{(0,0)} ⇝ T^{(1,1)}T^{(r)}$
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 1
SP - 5
EP - 16
AB - We study the problem of how a map f:M → ℝ on an n-manifold M induces canonically an affinor $A(f): TT^{(r)}M → TT^{(r)}M$ on the vector r-tangent bundle $T^{(r)}M = (J^r(M,ℝ)₀)*$ over M. This problem is reflected in the concept of natural operators $A:T^{(0,0)}_{|ℳ fₙ} ⇝ T^{(1,1)}T^{(r)}$. For integers r ≥ 1 and n ≥ 2 we prove that the space of all such operators is a free (r+1)²-dimensional module over $^{∞}(T^{(r)}ℝ)$ and we construct explicitly a basis of this module.
LA - eng
KW - bundle functors; natural transformations; natural operators
UR - http://eudml.org/doc/285093
ER -