Blow-ups of Lie groupoids and Lie algebroids
Lennart Obster

TL;DR
This thesis thoroughly explains and compares various methods for constructing blow-ups of Lie groupoids and Lie algebroids, providing new insights and unifying different approaches within a geometric framework.
Contribution
It offers a detailed exposition of existing blow-up constructions for Lie groupoids and algebroids, and introduces a general geometric blow-up construction that unifies previous methods.
Findings
Unified blow-up construction for Lie groupoids and algebroids.
Demonstrated Morita invariance of the blow-up construction.
Provided explicit examples including blow-ups along submanifolds and leaves.
Abstract
In this master's thesis, we will go into the (projective) blow-up construction for Lie groupoids and Lie algebroids. In the literature, there are different methods to be found on how to do this, especially for Lie groupoids. The main goal of the thesis is to explain, in detail, the Lie groupoid and the Lie algebroid blow-up constructions, but also to examine and compare different points of view. More explicitly, we will rigorously explain the blow-up construction for Lie groupoids by Claire Debord and Georges Skandalis. Moreover, we will show that the blow-up construction for Lie groupoids by Songhao Li and Marco Gualtieri, and the construction by Kirsten Wang, fit into this setting. Also, we will show that, analogously, we obtain a general geometric blow-up construction for Lie algebroids. This construction for Lie algebroids coincides with the construction of lower elementary…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
