<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        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
        votes
        0answers
        35 views

        Holomorphic foliation and Morse-Bott function

        Let $f$ be a holomorphic Morse-Bott function on a complex manifold $X$, with critical points being a compact complex manifold $Y$. Here Morse-Bott means the Hessian of $f$ is non-degenerate in the ...
        9
        votes
        2answers
        640 views

        Is differential topology a dying field?

        I recently had a post doc in differential topology advise against me going into the field, since it seems to be dying in his words. Is this true? I do see very little activity on differential topology ...
        3
        votes
        1answer
        87 views

        Reduction of the structure group of $\mathbb{R}^n$-fiber bundles to a special subgroup of $\mathrm{Homeo}(\mathbb{R}^n)$

        Let $G$ be the group of all self-homeomorphisms $f$ of $\mathbb{R}^n$ which satisfy $$f(x+m)=f(x)+m,\quad \forall m\in \mathbb{Z}^n.$$ In other words, $G$ is the group of all equivariant self-...
        5
        votes
        1answer
        136 views

        Is $π:\mathcal{C}^∞(M,N)→\mathcal{C}^∞(S,N)$, $π(f)=f|_S$ a quotient map in the $\mathcal{C}^1$ topology?

        This question was previously posted on MSE. Let $M, N$ be smooth connected manifolds (without boundary), where $M$ is a compact manifold, so we can put a topology in the space $\mathcal C^\infty(M, N)...
        11
        votes
        2answers
        389 views

        Realizing cohomology classes by submanifolds

        In "Quelques propriétés globales des variétés différentiables", Thom gives conditions for a class in singular homology of a compact manifold to be realized by a smooth oriented submanifold (see e.g. ...
        2
        votes
        0answers
        74 views

        How much is the theory of piecewise-smooth manifolds different from the PL and smooth ones?

        There are many differences between the smooth manifolds category and piecewise linear manifolds category when it comes to classification, embedding of these manifolds inside each other or otherwise. ...
        10
        votes
        1answer
        331 views

        Example of two exotic closed 4-manifolds s.t. SW(X)=0

        I am interested in seeing examples of two closed 4-manifolds $X_1,X_2$ such that $SW(X_i)=0$ and they are homeomorphic but not diffeomorphic. So far in the literature I've only found examples which ...
        3
        votes
        2answers
        250 views

        Is Cohen immersion conjecture (theorem) known for vector bundles?

        R. Cohen proved the immersion conjecture in a 1985 Annals paper: Cohen, Ralph L., The immersion conjecture for differentiable manifolds, Ann. Math. (2) 122, 237-328 (1985). ZBL0592.57022. Any smooth ...
        -1
        votes
        0answers
        35 views

        Rado-Kneser-Choquet Theorem, surjectivity [closed]

        This question is there on MSE, but the answer (Comment mode) is not satisfactory. I tried to prove the surjectivity, but unable to complete my argument. It is clear that $f$ is a closed map, since $\...
        2
        votes
        1answer
        83 views

        Every symplectic submanifold is J-holomorphic

        I am trying to show that every symplectic submanifold $N$ of a 2n- dimensional symplectic manifold $(M,\omega)$ is J-holomorphic for some compatible almost complex structure $J$. The way I am ...
        3
        votes
        0answers
        41 views

        Minimum rank of inverse complex vector bundles

        When considering vector bundles (real or complex) over a compact manifold, i know about the existence of inverse bundles. That is, if $\xi$ is a vector bundle over $M$, then there is a bundle $\nu$ ...
        1
        vote
        1answer
        144 views

        A special non vanishing vector field on odd dimensional compact manifolds

        Edit: According to the comment of Michael Albanese we revise the question. Assume that $n$ is an odd integer and $M\subset \mathbb{R}^{2n}$ is a compact orientable $n$ dimensional submanifold. Does ...
        2
        votes
        0answers
        68 views

        Reference request; Hirsch's structure functors

        In Hirsch's Differential Topology book is decribed the notion of a structure functor (page 52 of the first edition). Subsequently appears a Globalization Theorem involving such functors. The ...
        2
        votes
        1answer
        98 views

        Do submersions induce open maps between spaces of differentiable maps?

        Let $X$, $Y$ and $Z$ be smooth manifolds. Any differentiable map $f \colon Y \rightarrow Z$ induces a continuous map $f_{\ast} \colon C^{\infty}(X, Y) \rightarrow C^{\infty}(X, Z)$ via composition $g \...
        4
        votes
        0answers
        150 views

        Is polar decomposition of a smooth map Sobolev?

        Motivation: Let $\mathbb{D}^2$ be the closed unit disk. I am studying the "elastic energy" functional $E(f)=\int_{\mathbb{D}^2} \text{dist}^2(df,\text{SO}_2)$, where $f \in C^{\infty}(\mathbb{D}^2,\...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>
                    太阳vs开拓者战绩 拳皇命运卢卡尔和疯娜哪个好 皇家社会对马德里竞技 法国第戎市 银弹电子 pp电子三只老虎技巧 剑网3指尖江湖公测2017 水果大战熊出没 波斯波利斯宫殿 全国pc蛋蛋计划