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      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”.

      3
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      55 views

      Globalising fibrations by schedules

      In a paper in Fund Math 130.2 (1988): 125-136. http://eudml.org/doc/211719 Dyer and Eilenberg give an account of the local-global theorem for fibrations by proving a "Schedule Theorem" that, given a ...
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      votes
      2answers
      661 views

      Examples of odd-dimensional manifolds that do not admit contact structure

      I'm having an hard time trying to figuring out a concrete example of an odd-dimensional closed manifold that do not admit any contact structure. Can someone provide me with some examples?
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      9 views

      Boundary value problems for differential inclusions with fractional order

      I'm having technical problems or just lack of knowledge problems, so I would appreciate your help. the problem:: let $v_{*}\in F$, and for every $w \in F$, we have $$|v_{n}-v_{*}| \leq |v_{n}-w|+|w-...
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      vote
      1answer
      92 views

      Classification of all equivariant structure on the Möbius line bundles

      Is there a classification of all equivariant structures of the M?bius line bundle $\ell\to S^1$?. For example the antipodal action of $\mathbb{Z}/2\mathbb{Z}$ on $S^1$ cannot be lifted to the total ...
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      votes
      0answers
      177 views

      Do smooth manifolds admit unique cubical structures?

      It seems to me that a smooth manifold should admit the structure of a cubical complex by Morse theory, since handle attachments seem to be perfectly cubical maps. Is this cubical structure "...
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      votes
      2answers
      305 views

      Is this a submanifold?

      Let $(M,g)$ be a compact Riemannian manifold with an isometric action $\rho : G \to \mathrm{Iso}(M)$ by a compact Lie group $G$. There is a natural extension of $\rho$ to $TM$ given by: $$\psi : G \...
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      votes
      1answer
      286 views

      Smooth vector fields on a surface modulo diffeomorphisms

      Let $\Sigma$ be a two-dimensional connected smooth manifold without boundary. (Feel free to assume it is compact and orientable.) Let $\mathcal{X}(\Sigma)$ denote the smooth vector fields on $\Sigma$...
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      votes
      1answer
      124 views

      $L^{2}$ Betti number

      Let $\tilde{X}$ be a non-compact oriented, Riemannian manifold adimits a smooth metric $\tilde{g}$ on which a discrete group $\Gamma$ of orientation-preserving isometrics acts freely so that the ...
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      206 views

      On the homotopy type of $\mathrm{Diff}(\mathbb{S}^3)$

      I am confused with the following argument. I know I am doing something wrong but I can't find my mistake. On one hand, one knows that if $M$ is a Lie group, then $$\mathrm{Diff}(M)\simeq M\times\...
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      1answer
      125 views

      Homology of universal abelian cover of a manifold

      If one define the universal abelian covering $M_0$ of a manifold $M$ as the abelian covering (i.e. normal covering with abelian group of deck transformations) that covers any other abelian covering, ...
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      votes
      0answers
      54 views

      Symplectic vector fields everywhere transverse to a co-dimension one hypersurface

      Usually when speaking about vector fields transverse to a hypersurface in a symplectic manifold, we talk about Liouville vector fields, i.e. vector fields $X$ with the property that $\mathcal{L}_X\...
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      votes
      0answers
      191 views

      What mathematical background to i need in order to understand proofs of the h-cobordism theorem?

      I am about to finish my undergraduate studies and I really enjoyed the topology and differential-geometry classes. I'd love to continue studying differentialtopology and i considered doing some ...
      2
      votes
      0answers
      62 views

      Transitivity of Diff on the space of embeddings of balls

      Given 2 symplectic embeddings $g_0$ and $g_1$ of a 4-ball of radius $r \leq 1$ into the 4-ball of radius 1 (all equipped with the standard symplectic form coming from $\mathbb{R}^4$), does there exist ...
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      votes
      1answer
      234 views

      Different definitions of the linking number

      Assume that $$ \iota_1:\mathbb{S}^k\to\mathbb{R}^n, \quad \iota_2:\mathbb{S}^\ell\to\mathbb{R}^n, \quad k+\ell=n-1, $$ are two embeddings of spheres with disjoint images $\iota_1(\mathbb{S}^k)\cap\...
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      0answers
      255 views

      History of the definition of smooth manifold with boundary

      I am trying to determine the earliest source for the definition of smooth ($C^\infty$) manifold with boundary. Milnor and Stasheff (1958) give a definition, but a scrutiny of that definition shows it ...

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