# 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).

**39**

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### Minimal volume of 4-manifolds

**38**

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### Homotopy type of TOP(4)/PL(4)

**36**

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### What is the three-dimensional hyperbolic volume of a four-manifold?

**30**

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### Metrics on the 3-sphere with knotted geodesics

**28**

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### Do there exist exotic 4-tori?

**24**

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### Exotic 4-spheres and the Tate-Shafarevich Group

**23**

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### Concordance and homology cobordism

**22**

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### Smooth thickenings of non-smoothable manifolds

**22**

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### Monoid structure of oriented manifolds with connect sum

**22**

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### Boundaries of noncompact contractible manifolds

**20**

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### Is the mapping class group of $\Bbb{CP}^n$ known?

**20**

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### Topological description of inverting a knot

**20**

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### The oriented homeomorphism problem for Haken 3-manifolds

**19**

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### Is there a simpler proof of the key lemma in the paper by Hiroshi Iriyeh and Masataka Shibata on the 3D Mahler conjecture?

**19**

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### Homeomorphisms of the sphere mapping a geodesic triangulation to another one

**19**

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### Which manifolds decompose into pants?

**19**

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### Polynomials with roots in convex position

**18**

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### “High-concept” explanation for proof of a theorem of Ochanine?

**18**

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### What do tangles teach us about braids?

**18**

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### Almost complex 4-manifolds with a “holomorphic” vector field

**17**

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### What is the centralizer of a Coxeter element?

**17**

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### Horrible sets and blowups in Hubbard's Teichmuller theory

**16**

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### Are these local systems on $\mathscr{M}_{g,1}$ motivic?

**16**

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### Finitely generated groups with Hölder-exotic space of ends?

**16**

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### Do TQFTs give a complete set of invariants of manifolds?

**15**

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### What is the determinant of Poincaré duality?

**15**

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### Does every connected set that is not a line segment cross some dyadic square?

**15**

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### Asymptotics for the number of triangulations of a manifold M

**14**

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### Hauptvermutung for non-manifolds

**14**

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

**14**

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### Are there Alexander-Whitney maps in geometric homology?

**14**

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### Is the group $\operatorname{Diff}^1_0(\mathbb R^d)$ connected?

**14**

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### Connected sum is well-defined for surfaces, proof?

**13**

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### A geometric interpretation of the odd-primary Kervaire elements

**13**

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### Log symplectic vortex equations in Hamiltonian log GW theory

**13**

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### Is there a Handle Approximation theorem?

**13**

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### reference - Grothendieck on Thurston's work

**13**

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### Structure of Gordian graph of knots

**13**

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### Aspherical manifold and non-positive curvature

**13**

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### What is the cup-product structure like on a hyperbolic 5-manifold?

**13**

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### pizza lemma (topology)

**13**

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### Which spherical space forms embed in $S^4$?

**13**

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### Approximating homeomorphisms of 2-disk by diffeomorphisms

**13**

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### rigidity of representations of dehn fillings on the figure eight knot

**12**

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### The $\infty$-category of $n$-manifolds and open embeddings determined homotopically from that of topological manifolds?

**12**

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### Finite list of neighborhoods to approximate any finite simplicial complex

**12**

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### Counter example to lifting contractibility of a topological space

**12**

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### If two group actions lead to the same orbifold, are they conjugate?

**12**

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### Define the 3d Chern-Simons TQFT on a discrete simplicial complex

**12**

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