University of Guilan Journal of Algebra and Related Topics 2345-3931 8 1 2020 06 01 Pullback of lie algebra and lie group bundles, and their homotopy invariance 15 26 4191 10.22124/jart.2020.13988.1156 EN K Ajaykumar School of PPSH, Chinmaya Vishwavidyapeeth, Adi Sankara Nilayam, Ernakulam, Kerala, India B. S. Kiranagi Department of Mathematics, University of Mysore,Mysuru R Rangarajan Department of Mathematics, University of Mysore, Mysuru Journal Article 2019 07 30 We study the pullback Lie algebra (group) bundle of a Lie algebra (group) bundle and show that the Lie algebra bundle of the pullback of a Lie group bundle $\mathfrak{G}$ is isomorphic to the pullback of the Lie algebra bundle of $\mathfrak{G}$. Then, using the notion of Lie connection on a Lie algebra bundle, we show that the pullbacks of a Lie algebra bundle $\xi$ over a smooth manifold $M$ with respect to two smooth homotopic functions $f_0 , f_1 : N \rightarrow M$ are isomorphic to Lie algebra bundles over $N$. https://jart.guilan.ac.ir/article_4191_3712eb10e7125bda991a9f59b3684336.pdf