All Questions

$\DeclareMathOperator\Diff{Diff}$Setting: Let $(M,g)$ be a compact and connected $C^{\infty}$-Riemannian manifold. Let $d_g$ denote the induced shorted path metric and equip $C^{\infty}(M)$ with the ...

Suppose $X, Y$ are compact sets in $\mathbb{R}^2$ and $F$ is an ambient isotopy carrying $X$ onto $Y$. Is there an ambient isotopy $F'$ agreeing with $F$ on $X$ and which is constant in a ...

The Thurston Polytope provides a way to organize information about the embedded surfaces living in a 3-manifold. His amazing theorem, often called the "Fibered Faces" Theorem, says that if you have ...

I'm trying to study the spectrum operator via Floer Theory. The idea is to consider the Rayleigh quotient as an operator on the Hilbert space $W^{1,2}$ and to study it's negative gradient flow. Any ...

Non-triviality of the Conley index for an isolating neighborhood $N$ and a flow $\varphi$ can be used to prove non-emptyness of the related isolated invariant set. In particular, if $N$ doesn't ...