# 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).

**10**

**1**answer

### Is there an orientable prime manifold covered by a non-prime manifold?

**6**

**1**answer

### Example of homeomorphism of $3$-manifolds

**0**

**1**answer

### Fixed points of diffeomorphisms of tori isotopic to identity and their traces under isotopies

**6**

**2**answers

### “Well-known fact” that every irreducible 3-manifold with non-empty boundary has an incompressible surface

**1**

**0**answers

### Knot traces and $4$-dimensional analogue of theorem of Lickorish and Wallace

**5**

**2**answers

### 3-colored triangulations of the sphere $S^2$, and Sperner's Lemma

**21**

**0**answers

### Curves on potatoes

**5**

**1**answer

### How does the scalar TV invariant of a 3-manifold with boundary fit into the TQFT picture?

**6**

**1**answer

### Subdivision of closed homology manifold reference request

**5**

**1**answer

### Constructing exotic $\mathbb{R}^4$'s using vector fields on $\mathbb{R}^5$

**0**

**0**answers

### Fundamental class of products of spaces [migrated]

**3**

**1**answer

### Geometric content of area of a word in geometric group theory?

**1**

**0**answers

### Is there an analogue of the Thurston norm for curves in an an arbitrary oriented 3-manifold?

**1**

**0**answers

### Mapping class groups of $T^2 \times [0, 1]$ and $T^2 \times S^1$

**8**

**3**answers

### Can triangulations (or some related combinatorial structure) distinguish smooth structures on $RP^4$?

**7**

**0**answers

### Small flag triangulations

**8**

**0**answers

### Rational cobordism classes of manifolds fibered over spheres

**4**

**0**answers

### Enlarging a compact set in order to improve its shape

**15**

**1**answer

### Sperner's Lemma implies Tucker's Lemma - simple combinatorial proof

**5**

**1**answer

### The metric difficulty of unknotting unknots

**3**

**0**answers

### (symplectic) $h$-cobordism from $S^1\times S^2$ to itself

**4**

**1**answer

### “Basic” loops on standardly embedded surfaces

**4**

**2**answers

### Is the intersection of two distinct sufficiently small metric spheres always empty, a point or a metric sphere of lower dimension?

**1**

**0**answers

### Convex surfaces with transverse boundary (contact geometry)

**10**

**0**answers

### Find a 4-manifold bounding a 3-torus with any abelian representation in SL_2

**6**

**1**answer

### Cobordism monopole Floer homology

**6**

**0**answers

### Computing $\pi_2$ of the complement of a 2-knot or spaces with aspherical splittings?

**3**

**0**answers

### Cobordism theory of some weird space

**6**

**2**answers

### Books on foliations

**6**

**1**answer

### Mean curvature flow and knot theory

**5**

**1**answer

### Whitney sum formula for topological Pontryagin classes

**1**

**2**answers

### Transverse invariant measures to vector fields

**64**

**30**answers

### Proofs where higher dimension or cardinality actually enabled much simpler proof?

**4**

**0**answers

### Image of the mapping class group of surfaces into automorphism group?

**3**

**1**answer

### Maximally symmetric hyperbolic 3-manifolds with finite volume

**1**

**0**answers

### When a free action gives rise to a $G$-principal bundle

**4**

**0**answers

### Implicit function theorem for PL maps

**6**

**0**answers

### Why does the inverse Alexander polynomial appear in the MMR conjecture?

**6**

**1**answer

### Solutions of PDE under changing topology

**3**

**0**answers

### Convergence of Fuchsian groups and existence of suitable homeomorphisms

**7**

**1**answer

### Retracting off a compact set

**4**

**1**answer

### Mirzakhani's hyperbolic method generalized to moduli space of stable maps

**4**

**3**answers

### Is it possible to connect every compact set?

**1**

**0**answers

### Spaces that are comparable with their compacts

**1**

**0**answers

### Spherical space-form as the boundary of an Euclidean ball

**2**

**0**answers

### Retracting to a bigger compact

**12**

**1**answer

### Powers of the Euler class, torsion free subgroup of Homeo($S^1$)

**3**

**1**answer

### Unknotting algorithm in higher dimensions?

**3**

**2**answers

### Homology torsion in the double branched cover of a tangle?

**2**

**0**answers