# 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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### Studying separating surfaces, is this geometry or topology? [on hold]

**9**

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### Reference request for wild 3-manifolds

**0**

**1**answer

### Maximum of a sum of Gaussian functions

**3**

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### Can bellows make loops?

**4**

**1**answer

### non-proper parabolic isometries of hyperbolic spaces

**5**

**1**answer

### Is there a generalized Property P - what can we say about framed link descriptions of $S^3$?

**10**

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### Is there a known invariant for knotted surfaces defined by skein relations?

**10**

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### Are there exotic twisted doubles of 4-manifolds?

**7**

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### Different definitions of Stiefel-Whitney classes

**10**

**1**answer

### Homeomorphic characterization of the real line? [duplicate]

**5**

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### "There exists $e_0(S)$ such that the shortest nonperipheral curve on $(S, x)$ has extremal length at most $e_0$

**5**

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### Is there any known relationship between sutured contact homology and Legendrian contact homology?

**8**

**1**answer

### Critical dimensions D for “smooth manifolds iff triangulable manifolds”

**6**

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### Adjoint of the Hodge de Rham star operator under the integral pairing

**4**

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### When Stone–Čech compactification is totally disconnected

**3**

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### If the total space of circle bundle over hyperbolic manifold admits Riemannain metric of non-positive sectional curvature?

**4**

**1**answer

### Flat solvmanifolds?

**2**

**1**answer

### Sheaves on solenoids

**10**

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### Triangulation of the complex projective plane

**11**

**2**answers

### Minimal area of Seifert surfaces

**9**

**1**answer

### An almost complex structure on $S^2\times …\times S^2 / \mathbb{Z_2}$

**3**

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### Topological approach to create a space between clouds

**4**

**1**answer

### Complement of Donaldson divisors in dimension 4

**6**

**1**answer

### Action of diffeomorphism group on non-vanishing vector fields

**4**

**2**answers

### Is the *unreduced* Burau representation unitary?

**8**

**2**answers

### Can one disjoin any submanifold in $\mathbb R^n$ from itself by a $C^{\infty}$-small isotopy?

**9**

**1**answer

### A wild embedding of $\mathbb{S}^1$ into $\mathbb{R}^3$

**6**

**1**answer

### Relationship between induced maps at homotopy groups level for maps $f:S^2\to S^2$

**4**

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### Mapping class group of $\mathbb{S}^3$

**6**

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### Hyperbolic group with boundary $S^1$ implies virtually Fuchsian via bounded cohomology?

**5**

**1**answer

### Approximate Homology of a Large Simplicial Complex

**8**

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### “Cross-Ratios” for D_n cluster algebra

**21**

**6**answers

### Smooth functions on sphere

**14**

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### Presenting 3-manifolds by planar graphs

**5**

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### Categorification-like statement in the cobordism group?

**0**

**1**answer

### Intersection of hyperspheres

**6**

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### Pin cobordism v.s. “KO” theory in low or in any dimensions

**6**

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### Arf-Brown-Kervaire invariant and a surjective map $G \to Pin^-$

**9**

**1**answer

### Discrete Pin structures

**5**

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### Triple data for Pontrjagin dual of the Spin bordism group

**5**

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### Induced new structures on Poincare dual manifolds

**5**

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### Elementary questions about Morse-Bott functions

**5**

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### Applications of E8 manifold

**8**

**2**answers

### Hyperbolic $3$-manifold groups that embed in compact Lie groups

**2**

**1**answer

### Structure sets for three dimensional surgery

**4**

**0**answers

### Does there exist a preferred trivialization of a trivial line bundle?

**6**

**2**answers

### Generalization of Bieberbach's second theorem

**6**

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### Cell structures of simply-connected 5-manifolds (classified by Barden's 1965 paper)

**4**

**1**answer

### A combinatorial gadget for smoothly slice knots

**6**

**2**answers