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Results tagged with invariant-theory
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user 16702
Invariant theory deals with an algebraic, geometric or analytic structure $X$, submitted to the action of an (algebraic) group $G$. It studies $G$-invariant elements of $X$ as well as the set of $G$-orbits.
9
votes
0
answers
439
views
Invariant polynomials in curvature tensor vs. characteristic classes
Let $M$ be an $4m$-dimensional Riemannian manifold. We can then form the Pontryagin classes $p_k(TM)$ of the tangent bundle using Chern-Weil theory. For any sequence of numbers $k_1, \dots, k_l$ such …
- 9,853
5
votes
Accepted
What are all invariant polynomials on the space of algebraic curvature tensors?
I am not sure that this has a "nice" answer. Your question can be reformulated as follows. Let $\mathcal{A}_n$ be the space of algebraic curvature tensors on $\mathbb{R}^n$. A homogenous polynomial $P …
- 9,853
3
votes
1
answer
241
views
Invariance group of Morse charts
Suppose I have a smooth function $\varphi$ that vanishes at $p$ and has a positive definite Hessian at that point (suppose that we are on a smooth manifold of dimension $M$). Then the Morse lemma tell …
- 9,853