scholarly journals Lie Algebroids, Holonomy and Characteristic Classes

2002 ◽  
Vol 170 (1) ◽  
pp. 119-179 ◽  
Author(s):  
Rui Loja Fernandes
Keyword(s):  
Lie Algebroids ◽  
Characteristic Classes

scholarly journals Obstructions for Symplectic Lie Algebroids

2020 ◽  
Author(s):  
Ralph L. Klaasse ◽  
◽  
◽  
Keyword(s):  
Lie Algebroids ◽  
Characteristic Classes ◽  
Poisson Structures ◽  
Symplectic Structures ◽  
Topological Obstructions

Several types of generically-nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, b<sup>k</sup>-, scattering and elliptic-log Poisson structures. In this paper we discuss topological obstructions to the existence of such Poisson structures, obtained through the characteristic classes of their associated symplectic Lie algebroids. In particular we obtain the full obstructions for surfaces to carry such Poisson structures.

Chern–Simons forms for ℝ-linear connections on Lie algebroids

2018 ◽  
Vol 29 (13) ◽  
pp. 1850094
Author(s):  
Bogdan Balcerzak
Keyword(s):  
Chern Character ◽  
Lie Algebroids ◽  
Characteristic Classes ◽  
Linear Connections ◽  
Secondary Characteristic Classes ◽  
Chern Simons ◽  
Secondary Characteristic

This paper considers the Chern–Simons forms for [Formula: see text]-linear connections on Lie algebroids. A generalized Chern–Simons formula for such [Formula: see text]-linear connections is obtained. We apply it to define the Chern character and secondary characteristic classes for [Formula: see text]-linear connections of Lie algebroids.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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