Questions tagged [gt.geometric-topology]
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
4,448 questions
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Triangulated manifolds with local orientation reversal
For a (smoothly) triangulated $n$ manifold $M$, I'll say that the triangulation is amphichiral if it admits an orientation-reversing automorphism. I'll say that the triangulation is locally ...
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What is the volume of $\Sigma(2, 3, 13)$ associated with its $\widetilde{\operatorname{SL}(2, \mathbb{R})}$ geometry?
I've been considering a research topic based on extending the material from Khoi's research paper concerning a Chern–Simons-type invariant for 3-manifolds, and I'm stuck on a specific problem ...
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chain level intersection product
Let $F$ be a field and $M$ an oriented smooth $n$-manifold.
Is it always possible to construct a differential graded $F$-vector space $(C_M,d)$ equipped with a strictly coassociative coproduct $\Delta ...
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Isotopy to achieve finite intersections
I've asked this question on math.stackexchange a week ago, with no response. More context is available there.
Suppose that $\alpha$ and $\beta$ are closed curves on the $2$-manifold, say $F$ (possibly ...
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cellular and handle chain complex of universal covering
Let $M$ be a compact connected smooth manifold with fundamental group $\pi:=\pi_1(M)$ and universal covering $\widetilde{M}$. We can equip $M$ with a handle decomposition and we obtain the handle ...
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Generalized manifolds similar to stratifolds
Let $S_n = [0, \infty)^n \setminus (0, \infty)^n \subset \mathbb{R}^n$ be the union of coordinate hyperplanes in the non-negative orthant. We equip $S_n$ with an enlarged topology $\tau^*$ rather than ...
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When is a symplectic manifold with the opposite orientation itself symplectic?
Suppose $(M,\omega)$ is a closed (compact without boundary) symplectic manifold of dimension $2n$. Suppose $\overline{M}$ is a homeomorphic copy of $M$ with the opposite (reverse) orientation. My ...
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Relationship between parametric pseudo-manifolds (Gallier) and topological pseudomanifolds
I am interested in the relationship between the concept of a Parametric pseudo-manifold (PPM), as defined by Jean Gallier ,Dianna Xu, Marcelo Siqueira (e.g., in "Parametric pseudo-manifolds",...
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Is there a formula to compute the correction terms to Heegaard Floer homology for plumbed $3$-manifolds?
If $Y$ is a rational homology three sphere, the correction term $d(Y, \mathfrak{s})$ to Heegaard Floer homology is defined as the minimal $\mathbb{Q}$-degree of any non-torsion class in $HF^{+}(Y, \...
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New geometric homology theory
Let $S_n = [0, \infty)^n \setminus (0, \infty)^n \subset \mathbb{R}^n$ be the union of the coordinate hyperplanes in the non-negative orthant. We consider a smooth structure on $S_n$ defined by local ...
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Is Ramanujan's $G_{1255}$ connected to the snub dodecadodecahedron?
I. Polyhedra
In this MO question and the table below it, we checked all 75 uniform polyhedra and found that of the 12 uniform snub polyhedra, then TEN have Cartesian coordinates involving constants ...
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Is there Pachner theory for simplicial sets?
Pachner moves can be defined as follows: Pick an $n+1$-dimensional simplex and cut its boundary in two parts. Take an $n$-dimensional PL manifold with a triangulation, look for a place in the ...
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Controlled topology of Casson handles
There is a theorem by M. Friedman that every Casson handle is standard.
Q: can this be made Hölder?
The answer is probably negative( although I do not see the proof at the moment, would be nice to ...
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Under what conditions does homeomorphism $X^o\simeq Y^o$ imply $\partial X\simeq \partial Y$?
Let $X$ and $Y$ be smooth compact manifolds with boundary. Assume that $X\setminus \partial X$ is homeomorphic to $Y\setminus \partial Y$.
Under what conditions can one conclude that $\partial X$ is ...
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On Existence of Certain Types of Flow on Locally Compact Spaces in $\mathbb{R}^n$
Given an $n$-dimensional, locally compact $X \subset \mathbb{R}^{2n+1}$ under what conditions does there exist a flow via ambient homeomorphisms $[0, \infty) \times \mathbb{R}^{2n+1} \rightarrow \...
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