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Analogue of $O(n) \subset GL(n,\mathbb{R})$ in $Diff, PL, TOP$

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#algebraic-topology #topological-groups #geometric-topology
1.2k
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Why is the hyperbolic plane homeomorphic to $\mathbb{R}^2$, whilst the 2-sphere isn't?

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#general-topology #hyperbolic-geometry #geometric-topology #noneuclidean-geometry
167
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Surgery on $S^3$

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#general-topology #algebraic-topology #differential-topology #geometric-topology #surgery-theory
380
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Comprehensive textbook in surgery theory

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#reference-request #geometric-topology #surgery-theory
88
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What is the type of this surface?

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#algebraic-topology #surfaces #geometric-topology
124
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What is a non-complete simple geodesic on closed hyperbolic surface?

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#hyperbolic-geometry #geometric-topology
2.6k
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How to visualize the real projective plane $\mathbb RP^2$ in three dimensions, if possible?

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#geometric-topology
148
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Is $S^2$ homeomorphic to $X \times X$?

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#general-topology #algebraic-topology #geometric-topology
81
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Figuring out a group in a short exact sequence

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#abstract-algebra #group-theory #geometric-topology #exact-sequence
571
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Hyperbolic Right-Angled Hexagon

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#geometry #reference-request #hyperbolic-geometry #geometric-topology
183
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Covering a Hyperbolic Right-Angled Hexagon

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#geometry #trigonometry #hyperbolic-geometry #geometric-topology #hyperbolic-functions
335
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Lifts of flows to the universal cover

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#differential-geometry #differential-topology #dynamical-systems #geometric-topology #vector-fields
6.6k
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Why is this discrete subgroup of $PSL(2,\mathbb{C})$ not Kleinian?

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#complex-analysis #riemannian-geometry #riemann-surfaces #geometric-topology #modular-group
52
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1D Topological manifold that is not $\mathcal{C}^r$?

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#proof-verification #manifolds #differential-topology #smooth-manifolds #geometric-topology
33
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Fully compressing a surface in a 3-manifold

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#differential-topology #geometric-topology

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