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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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      Geometry of a manifold after Dehn filling, in terms of geometry pre-filling

      First time posting, so sorry if this is an uninteresting or overly long post! The inspiration for this question was sparked by this answer given by Bruno Martelli in response to a question about ...
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      28 views

      Model for random graphs where clique number remains bounded

      In the Erd?s-Rényi model for random graphs,the clique number is seen to go to infinity al the number of vertices grows. Is anyone aware of models for random graphs with bounded ...
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      153 views

      Cobordism modelling fibration over $S^1$

      Let $X$ be a closed oriented manifold which is a fibration over $S^1$ whose fiber $F$ is connected, i.e. $X\cong F\times[0,1]/\sim h$, for an $h\in \mathrm{Diff}(F)$. Suppose that $b_1(X)=1$. ...
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      Vietoris-Rips complex and coarse geometry

      Let $K$ be an infinite countable subset of Euclidean space $E$ such any point of $E$ is within distance 1 of some point of $K$. In the language of John Roe's "coarse geometry", this implies that $K$ ...
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      86 views

      Easy lemma for trivalent graphs in colored Jones polynomial

      In his 2008 paper, Tanaka, Toshifumi, The colored Jones polynomials of doubles of knots, J. Knot Theory Ramifications 17, No. 8, 925-937 (2008). ZBL1149.57023. Tanaka stated a lemma (Lemma 3.3) ...
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      50 views

      Second cohomology of handlebody mapping class group

      Let $H$ be a genus $g$ handlebody, let $\mathrm{Mod}(H)$ be its mapping class group. Is the calculation of $H^2(\mathrm{Mod}(H),\mathbb{Z})$ known? (Let $S$ be the boundary of $H$, then $\mathrm{Mod}(...
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      59 views

      Are Seifert fibered spaces with a horizontal surface exactly the surface bundles over the circle with periodic monodromy?

      Are Seifert fibered spaces with a horizontal surface exactly the surface bundles over a circle with periodic monodromy? I am unsure of my arguments for this: If a SFS has a horizontal surface then ...
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      113 views

      Starting letters of equivalent infinite geodesic paths of hyperbolic Coxeter groups

      Let $\left(W\text{, }S\right)$ be a Gromov hyperbolic Coxeter system and denote by $\partial W$ the corresponding Gromov boundary. For $z\in\partial W$ let $\alpha$, $\beta$ be infinite geodesic paths ...
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      Cyclic homotopies of quotients of $S^3$

      We are given a free action of an abelian finite group on $S^3$. Let $L$ denote the quotient space and let an element $\alpha \in \pi_1 L =G$ be given. Does there exist a cyclic homotopy $h_t:L \to L$ ...
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      225 views

      Is there a Morita cocycle for the mapping class group Mod(g,n) when n > 1?

      Write Mod(g,n) for the mapping class group of a genus-$g$ surface $\Sigma$ with $n$ boundary components. When $n=0,1$ we define the Torelli group $T$ to be the subgroup of Mod(g,n) which acts ...
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      Knot and its embedded disk

      Let $K \subset S^3$ be an arbitrary knot. Let $D$ denote the embedded disk in $B^4$ bounded by $K$. Up to diffeomorphism, is it possible to describe the followings (at least for some trivial knots, ...
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      1answer
      418 views

      Examples of hyperbolic groups

      What are some other classes of word-hyperbolic groups other than the finite groups, fundamental groups of surfaces with Euler characteristics negative and virtually free groups?
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      67 views

      Branched 2-fold covering over edge of a 3-orbifold

      I am reading the paper "On some generalized triangle groups and three-dimensional orbifolds" by Vinberg, Mennike and Khelling (Tran. Moscow Math. Soc. 1995 (56)). Let $k,l,m>0$, at most one of ...
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      Trajectory definition using constrained projections on unknown surface

      In $3D$ space where the $Z$ axis is up-down, I have the following: A static camera $A$ at $(x_a, y_a, z_a)$; A laser pointer $B$ at $(x_a, y_a, z_a + b)$ which can yaw or pitch by $1^\circ$ at a ...
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      114 views

      What is the connection between $\mathrm{AdS}_2$ and the hyperbolic plane $\mathbb{H}^2$?

      What is the connection between $\mathrm{AdS}_2$ and the hyperbolic plane $\mathbb{H}^2$? Some sources seem to imply that they are the same, i.e. having at least the same symmetry group $\mathrm{SL}(2,...

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