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        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).

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        Hyperbolic 3 manifold with trivial deformation of flat conformal structures

        Does there exist closed hyperbolic three manifold which is locally rigid in the space of its all conformally flat structures? If so could someone provide examples?
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        Hilbert space compression of lamplighter over lamplighter groups

        $C_2 \wr \mathbb{Z}$ is the lamplighter group but I'm currently looking at the lamplighter group with this group as a base space. Question: Consider the group $C_2 \wr (C_2 \wr \mathbb{Z})$, what is ...
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        Contractible affine surfaces of log Kodaira dimension 2

        The first examples of contractible smooth affine algebraic surfaces (over the complex numbers) of log Kodaira dimension 2 were constructed in a famous paper of Ramanujam https://www.jstor.org/stable/...
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        Chirality and Anti-Chirality of links in 3 and in 5 dimensions

        We know there is a chiral knot which is a knot that is not equivalent to its mirror image. It is well known in the mathematical field of knot theory: https://en.wikipedia.org/wiki/Chiral_knot My ...
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        97 views

        Regina and SnapPy

        I have been doing some statistical studies on small 3-manifolds, and I note that one can produce larg-ish censuses of triangulations in Regina. Now, the Regina documentation tells us how to convert a ...
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        Zero surgery on a Seifert fiber space

        I have a problem with understanding what is a neighbourhood of a singular fiber in a Seifert fibered space coming from the zero surgery. For me a 3-manifold $Y$ is a SFS if it has a decomposition into ...
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        Simple homotopy equivalent $3$-manifolds [duplicate]

        Let $M^3$ and $N^3$ be two oriented closed $3$-manifolds which are simple homotopy equivalent. Are $M^3$ and $N^3$ diffeomorphic? I was told that this follows from the geometrization conjecture, but I ...
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        $h$-cobordism between two spherical space forms

        Let $S^3/\Gamma_1$ and $S^3/\Gamma_2$ be two spherical space forms where $\Gamma_1$ and $\Gamma_2$ are finite subgroups of $SO(4)$ acting freely on $S^3$. Suppose $S^3/\Gamma_1$ and $S^3/\Gamma_2$ ...
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        137 views

        Isometries between spherical space forms

        Let $S^n/\Gamma_i\,(i=1,2)$ be a $n$-dimensional spherical space form, where $\Gamma_i \subset SO(n+1)$ is a finite subgroup acting freely on $S^n$. Suppose $S^n/\Gamma_1$ is diffeomorphic to $S^n/\...
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        1answer
        59 views

        Is transverse measure on a foliation without closed leaves unique?

        Let $(F,\nu)$ be a Thurston's foliation on a surface $S$ with a non-zero transverse measure $\nu.$ Assume that $F$ has no closed leaves nor compact separatrices. Did anyone study such foliations? ...
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        Classification of surface curves? [duplicate]

        Having a genus $g$ closed orientable surface $\Sigma$ (connected sum of $g$ tori), how do I encode any embedded closed curve up to planar isotopy? For $g=1$ we can just state the coefficient $k \in \...
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        118 views

        Reducing curves in surfaces by Dehn twists

        Let $F$ be a compact, oriented surface. A Dehn move, $D_\beta$, on a simple closed curve (scc) $\alpha$ is a Dehn twist applied to $\alpha$ along a scc $\beta$ which intersects $\alpha$ once. Is ...
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        64 views

        Homotopy classes of maps between special unitary Lie group. Correction [duplicate]

        An hour ago I asked a question (under the same title) but I used a wrong notation. Here is the improved version. We consider a special unitary Lie group $SU(n)$. Then its center is $\mathbb{Z}_n$ and ...
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        Action of the symmetric group on connected sums of manifolds (minus a disk)

        Let $M$ be a connected compact topological $n$-dimensional manifold without a boundary and with a CW-structure $M= \bigcup M^i$. We have that $$ (\#^g M)\smallsetminus D^n \simeq \bigvee_{i=1}^gM^{n-...
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        1answer
        201 views

        Homotopy classes of maps between special unitary Lie groups

        I am sorry to mislead the notations: $SU(n)$ should be replaced by $PSU(n)$. I will reformulate it now. We consider the special unitary Lie group $SU(n)$. Then its center is $\mathbb{Z}_n$ and we ...

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