# Questions tagged [differential-topology]

The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

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### Local coordinates of one form on a principal bundle

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### Restrictions on pointed lifts of isometries

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### Extending an embedding with trivial normal bundle

**19**

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### Can the product of a 3-dimensional lens space with a circle be diffeomorphic to another such product when the lens spaces aren't diffeomorphic?

**2**

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### Diffeomorphism classification of manifolds with fundamental group $\mathbb{Z}_n$, $n>2$

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### What locales correspond to Manifolds?

**8**

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### Degree one self-map of $\Bbb R^2\big\backslash \big\{(n,0):n\in \Bbb Z\big\}$ not homotopic to any self-homotopy equivalence

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### Uniqueness of collar neighborhoods for non-compact boundary case in smooth setting

**15**

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### Is there a $4$-manifold which Immerses in $\mathbb{R}^6$ but doesn't Embed in $\mathbb{R}^7$?

**8**

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### Non orientable, closed manifold covered by two contractible charts

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### Questions about a paper by Laudenbach and Poénaru

**4**

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### Existence parallel vector fields and its effect on the topology of manifolds (Karp's Thesis)

**16**

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### Reference request: Milnor rank of spheres

**3**

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### Existence of a certain foliation of $\mathbb R^n$

**2**

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### The topology of spaces of immersed circles in the plane

**3**

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### Existence of developable ribbonization of a surface

**1**

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### Looking for a criterion for a subset of a complex variety to be of measure zero

**6**

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### Dehn surgery along primitive knot in 3-dimensional handlebody

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### Is each Lipschitz action of a finite group on the 3-sphere equivalent to a linear action?

**6**

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### Godbillon–Vey invariant and leaf space of foliations

**2**

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### Collar neighborhood theorem for manifold with corners

**4**

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### Existence non-trivial parallel $p$-form implies non-triviality of $p$-th cohomology group using De Rham cohomology

**4**

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### Classification of square roots of line bundles and metalinear/metaplectic structures

**1**

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### Density of $G$-invariant morse functions

**9**

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### Local topology of Whitney stratified spaces

**0**

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### Antisymmetric tensor coordinates and tensorial spaces

**1**

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### Fiberwise starshaped Hypersurfaces in $T^*M$

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### Subset of the domain of attraction

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### singular homology of manifold with corners

**1**

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### Reference for non-parallel harmonic $k$-forms

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### Equivariant smooth approximation

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### Spin structures induced on embedded circles and choices of trivialisations

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### Existence of closed transversals for taut foliations in arbitrary codimension

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### Is $U(n)$ a Kahler manifold?

**15**

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### Examples of Banach manifolds with function spaces as tangent spaces

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### Fixed point set of diffeomorphism is a submanifold

**4**

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### restricting the “Whitney” map

**1**

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### Simple properties of the codifferential

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### Almost isometric manifolds are diffeomorphic

**2**

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### Blowing up the zero section for “Chasse au Canard” (some new kind of geometric canards)

**4**

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### Condition for existence of a continuous function realizing a partition

**2**

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### Clarification of different notions of spin structures

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### Stokes's theorem for pseudo-differential forms

**2**

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### Approximating continuous functions via diffeomorphisms on compact manifolds

**1**

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### Diffeomorphic excision of a manifold

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### Smooth dual cell structure

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### What is known about this conjectured symmetry in the generalized Radon-Hurwitz numbers?

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### Elementary proof of an inequality for the Radon-Hurwitz numbers

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### Quotients of a fixed manifold by a fixed Lie group

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