Questions tagged [stratifications]
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Is there a canonical smooth structure on tame Fréchet orbit type stratifications?
In finite dimension orbit type stratifications, it is known that the orbit space $M/G$ resulting from an action of a proper Lie Group $G$ on a smooth manifold $M$, satisfying a set of certain ...
- 808
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How to chart tubes around manifolds with boundary/corners?
Let $M \subset \mathbb{R}^d$ be a manifold with boundary/corners. For example, a piece of curve with endpoints or a $2d$ unit square in $\{ z = 0 \}$. I am interested in introducing local coordinates ...
- 600
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Extension of isotopies
In what follows $M$ will be a manifold (without boundary, for simplicity) and $C\subseteq M$ will denote a compact subset. In the paper Deformations of spaces of imbeddings Edwards and Kirby prove the ...
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If a subset $X$ of a $C^k$ manifold $M$ is semialgebraic in the charts of $M$, is it Whitney stratifiable?
Let $M$ be a $C^k$ manifold for some $k\geq 1$ and $X$ be a subset of $M$.
Assume that there is an atlas of charts $(\phi_\alpha, U_\alpha)_\alpha$ of $M$ such that in the coordinates of each of these ...
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Torsion in the spectral sequence for a stratified complex variety
Let $X$ be a (possibly singular) complex projective algebraic variety, endowed with a stratification $\{X_{\Delta}\}_{\Delta\in I}$ by smooth algebraic varieties.
Then there is a spectral sequence
$$...
- 718
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Smooth extension of piecewise smooth function on a corner
Imprecise Question: Suppose I have a function defined on non-codimension-zero strata of a smooth manifold with a stratification, and I know the function is smooth when restricted to each of these ...
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Under what assumption on a proper map does the preimage of sufficiently small neighborhood is homotopy equivalent to the fiber?
Let $\pi\colon X\rightarrow Y$ be a proper map of topological spaces. Let's assume that both $X$ and $Y$ are paracompact, Hausdorff and locally weakly contractible. Then is it enough to conclude that ...
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Stacks v.s. Stratifolds?
Both stacks and stratifolds can model spaces with singularities (say, singular quotient space for example). In my little experience, stacks are widely used in moduli problems and stratifolds are often ...
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Connected components of Isotropy types as strata of Poisson leaves
Let $X$ be a smooth affine variety with an algebraic symplectic form $\omega$. Let $G$ be a finite subgroup of the group of symplectomorphisms of $X$.
We can say that $X$ is trivially a normal variety ...
- 599
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Smooth affine variety as a symplectic resolutions
Given a smooth affine variety $X$ over $\mathbb C$ with an algebraic symplectic form $\omega$ and a finite group $G$ acting on $X$ by symplectomorphisms, then
Is it true that $X$ is trivially a ...
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Exit path categories of regular CW complexes
Given a finite, regular CW complex $X$ (by regular, I mean that the gluing maps $D^n \to X$ from the closed unit ball to $X$ are homeomorphisms onto their image), denote by $S$ the finite partially ...
- 894
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Topology types in families of real or complex varieties
In René Thom, "Structural Stability and Morphogenesis" on p. 21ff there is the following statement: Let
$$P_j(x_i,s_k) = 0$$
be a set of polynomial equations over the real or complex numbers,...
- 650
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Comparing the exit path category and the nerve of a stratified space
Let $P$ be a finite poset, and $X$ be a topological space stratified by $P$, in the sense that $X$ is equipped with a continuous map $X \to P$ in the Alexandroff topology (or equivalently with a ...
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On the zero-dimensional strata of the Fulton-MacPherson conpactification
Let $\operatorname{Conf}_n(\mathbb{R})$ be the configuration space of $n$ marked points on the real line. What is the difference between $\operatorname{Conf}_n(\mathbb{R})$ and the locus of zero-...
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Riemann-Hilbert-type correspondence for locally constant factorization algebras
This is related to a previous post, but a bit softer and should probably stand on its own.
In Appendix A of "Higher Algebra", Lurie shows that for a reasonably good topological space, there ...
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