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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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      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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      88 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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      votes
      2answers
      189 views

      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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      78 views

      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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      58 views

      $h$-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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      votes
      1answer
      135 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/\...
      1
      vote
      1answer
      58 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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      57 views

      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 \...
      3
      votes
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      116 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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      63 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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      79 views

      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
      197 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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      votes
      1answer
      245 views

      Laplacian spectrum asymptotics in neck stretching

      Let $M$ be a compact Riemannian manifold. Let $S \subset M$ be a smooth hypersurface separating $M$ into two components. Let $g_T$ be a family of Riemannian metric obtained by stretching along $S$, i....
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      96 views

      Which cubic graphs can be orthogonally embedded in $\mathbb R^3$?

      By an orthogonal embedding of a finite simple graph I mean an embedding in $\mathbb R^3$ such that each edge is parallel to one of the three axis. To avoid trivialities, let's require that (the ...
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      votes
      1answer
      143 views

      Hyperbolic Dehn surgeries and SU(2)-representations

      Let $S^3-K$ be the complement of the figure eight knot complement. Thurston, in his Lecture Notes, constructed a hyperbolic structure, which comes from a discrete, faithful representation $\pi_1(S^3-K)...

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