Natural maps on the iterated jet prolongation of a fibred manifold

1991 ◽  
Vol 158 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Ivan Kolář ◽  
Marco Modugno
Keyword(s):  
Natural Maps ◽  
Fibred Manifold ◽  
Jet Prolongation

scholarly journals On naturality of some construction of connections

2020 ◽  
Vol 74 (1) ◽  
pp. 57
Author(s):  
Jan Kurek ◽  
Włodzimierz Mikulski
Keyword(s):  
Linear Connection ◽  
Bundle Functor ◽  
Fibred Manifold ◽  
Natural Transformations ◽  
General Connection

Let \(F\) be a bundle functor on the category of all fibred manifolds and fibred maps. Let \(\Gamma\) be a general connection in a fibred manifold \(\mathrm{pr}:Y\to M\) and \(\nabla\) be a classical linear connection on \(M\). We prove that the  well-known general connection \(\mathcal{F}(\Gamma,\nabla)\) in \(FY\to M\) is canonical with respect to fibred maps and with respect to natural transformations of bundle functors.

Natural maps of extension functors and a theorem of R. G. Swan

1961 ◽  
Vol 57 (3) ◽  
pp. 489-502 ◽  
Author(s):  
P. J. Hilton ◽  
D. Rees
Keyword(s):  
Finite Group ◽  
Exact Sequence ◽  
Group Ring ◽  
Projective Module ◽  
Additive Group ◽  
Integral Group Ring ◽  
Integral Group ◽  
Natural Maps ◽  
Image Position ◽  
A Finite Group

The present paper has been inspired by a theorem of Swan(5). The theorem can be described as follows. Let G be a finite group and let Γ be its integral group ring. We shall denote by Z an infinite cyclic additive group considered as a left Γ-module by defining gm = m for all g in G and m in Z. By a Tate resolution of Z is meant an exact sequencewhere Xn is a projective module for − ∞ < n < + ∞, and.

A note on natural maps of higher extension functors

1963 ◽  
Vol 59 (2) ◽  
pp. 283-286 ◽  
Author(s):  
F. Oort
Keyword(s):  
Natural Maps ◽  
Image Position

Hilton and Rees have proved (cf. (1), Theorem 1·3) that every natural mapis induced by a map from A to B (or, Hom (A, B) → Next1,1 (A, B) is surjective). It follows that Ext1 (B, −) and Ext1 (A, −) are naturally isomorphic if and only if A and B are quasi-isomorphic (loc. cit., Theorem 2·6), i.e. if there exist projective objects P, Q and an isomorphism . One can ask whether these theorems remain true for higher extension functors.

scholarly journals The constructions of general connections on second jet prolongation

2014 ◽  
Vol 68 (1) ◽  
Author(s):  
Mariusz Plaszczyk
Keyword(s):  
Second Order ◽  
Linear Connections ◽  
Jet Prolongation ◽  
Torsion Free ◽  
Natural Operators

AbstractWe determine all natural operators D transforming general connections Γ on fibred manifolds Y → M and torsion free classical linear connections ∇ on M into general connections D(Γ,∇) on the second order jet prolongation J2Y → M of Y → M

scholarly journals The induced connections on total spaces of fibred manifolds

2015 ◽  
Vol 97 (111) ◽  
pp. 149-160
Author(s):  
Włodzimierz Mikulski
Keyword(s):  
Linear Connection ◽  
Linear Connections ◽  
Fibred Manifold ◽  
Torsion Free ◽  
General Connection

Let Y ? M be a fibred manifold with m-dimensional base and n-dimensional fibres. If m ? 2 and n ? 3, we classify all linear connections A(?, ?, ?) : TY ? J1(TY ? Y) in TY ? Y (i.e., classical linear connections on Y) depending canonically on a system (?, ?, ?) consisting of a general connection ? : Y ? J1Y in Y ? M, a torsion free classical linear connection ? : TM ? J1(TM ? M) on M and a linear connection ? : V Y ? J1(VY ? Y ) in the vertical bundle VY ? Y.

Natural maps depending on reductions of frame bundles

2011 ◽  
Vol 102 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Ivan Kolář
Keyword(s):  
Natural Maps
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