All Questions
Tagged with dg.differential-geometry invariant-theory
7 questions with no upvoted or accepted answers
9
votes
0
answers
449
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
7
votes
0
answers
236
views
Chern-Weil theory on some noncompact groups, and characteristic classes in differential cohomology
$\newcommand{\Z}{\mathbb Z}\newcommand{\HdR}{H_{\mathrm{dR}}} \newcommand{\Sym}{\mathrm{Sym}}
\newcommand{\g}{\mathfrak g}$I have a specific question about invariant polynomials for some Lie groups,
...
- 6,881
7
votes
0
answers
225
views
Relation between Donaldson invariants and GW invariants
What is known about the relation of Donaldson invariants on a complex surface $\Sigma$ and GW invariants (or equivalent) of local Calabi-Yau 3folds such as the canonical bundle of $\Sigma$? (if any of ...
- 661
3
votes
0
answers
127
views
Orbit space of the action of $\mathrm{GL}(V)$ on the Grassmannian of $V\wedge V$
$
\newcommand{\K}{\mathbb{K}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Grass}{Grass}
$Consider $\K\in\{\R,...
- 126
1
vote
0
answers
105
views
Codimension of cusp singularities in the space of 2-jets
In trying to prove Cerf's theorem about homotopies between Morse-functions I ended up thinking about the following problem.
For $n>2$, $a= (a_{i,j})\in GL(n-2)$, we define the polynomial map $C_a:\...
- 2,533
1
vote
0
answers
137
views
Invariant subspace of a nonlinear map
First please see this very simple fact:
Fact: $\ $ Any linear map $T: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ has a proper invariant linear subspace.
By an invariant subspace we mean a space $M$ ...
- 111
1
vote
0
answers
69
views
propagation of a invariance along some PDE
Consider the following non linear PDE on $\mathbb{R}^n$
$$ \partial_t u_t(x) \,=\, F\big(x, u_t(x), D u_t(x)\big)$$
with given initial condition $u_0(x)$.
Assume that:
$u_0$ is rotation invariant, ...
- 11