Gabriel Araújo’s articles on arXiv- Global solvability and cohomology of tube structures on compact manifolds
- Global analytic hypoellipticity and solvability of certain operators subject to group actions
- Global solvability and propagation of regularity of sums of squares on compact manifolds
- Global hypoellipticity of sums of squares on compact manifolds
- Periodic trajectory tracking for control-affine driftless systems on compact Lie groups
- Computing cohomology spaces of left-invariant involutive structures on $\mathrm{SU}(2)$: examples
- Global regularity and solvability of left-invariant differential systems on compact Lie groups
- Regularity and solvability of linear differential operators in Gevrey spaces: omitted proofs
Category Archives: Exercises
Invariance of domain and its friends
We recall the theorem on invariance of domain and derive some of its variants. We’ll follow J. Vick’s Homology Theory: An Introduction to Algebraic Topology (2nd edition). The invariance of domain is stated as follows: Theorem. Suppose that are homeomorphic … Continue reading
Posted in Exercises, Theorems
Tagged algebraic topology, invariance of domain, topology
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A simple exercise about abelian groups
Let be a group. Suppose there is an integer such that for . Prove that is abelian. Solution. Let . By we have . On the other hand we have where we have used again to obtain the last equality. … Continue reading
Gabriel Araújo 