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...f theorem''' (named after [[Heinz Hopf]]) is a statement in [[differential topology]], saying that the [[degree of a continuous mapping|topological degree]] is * {{cite book|last=Milnor|first= John W.|authorlink=John Milnor|title=Topology from the Differentiable Viewpoint|publisher=[[Princeton University Press]]| ...

In mathematics, the '''twisted Poincaré duality''' is a theorem removing the r ...theorem with real coefficients features [[de Rham cohomology]] with values in the '''orientation bundle'''. This is the '''[[flat vector bundle|flat]]''' ...

...owing that a distance-preserving map, which is a priori only [[continuity (topology)|continuous]], is actually [[Differentiable function|differentiable]]. ...row M</math> is <math display="inline">\mathcal{C}^1</math>differentiable (in both variables). This is a generalization of the easier, similar statement ...

In [[differential topology]], the '''transversality theorem''', also known as the '''Thom transversali ..., denoted as <math>f \pitchfork Z</math>, if and only if for every <math>x\in f^{-1}\left(Z\right)</math> we have that ...

...ng his plenary address at the [[International Congress of Mathematicians]] in [[Nice]]. Are the equators in <math>\mathbb{S}^{n+1}</math> the only smooth embedded minimal hypersurface ...

...linear map between Fréchet spaces and wishes to show that it is surjective in order to use the open mapping theorem to deduce that it is also an open map ...\to X^{\prime}</math> will be [[injective]], but the converse is not true in general. ...

...n |authorlink=Jean Dieudonné|title=A History of Algebraic and Differential Topology, 1900 - 1960 |date=2009 |publisher=[[Springer Science+Business Media|Spring ==Integral theorems== ...

In [[mathematics]], the '''pseudoisotopy theorem''' is a theorem of [[Jean Cer ...fnof;'' preserves the level-sets <math>M \times \{t\}</math> for <math> t \in [0,1]</math>. ...

{{Short description|Mathematical result about equivariant K-theory in homotopy theory}} ...''' is a [[theorem]] in [[mathematics]] about [[equivariant]] [[K-theory]] in [[homotopy theory]]. Let ''G'' be a [[compact group|compact]] [[Lie group]] ...

In [[differential geometry]], a field of mathematics, the '''Lie–Palais theorem''' is a parti ...th>a (\alpha) = d_e \Phi (\cdot,x) (\alpha)</math> for every <math>\alpha \in \mathfrak{g}</math>. ...

...logy]] about the topology of the space of [[Flat convergence|flat cycles]] in a Riemannian manifold. ...ar) [[Minimal surface|minimal submanifolds]] in every Riemannian manifold. In the special case of the space of null-homologous codimension 1 cycles with ...

...tion theorem''' is a [[selection theorem]] named after [[Ernest Michael]]. In its most popular form, it states the following:<ref>{{Cite journal | last1= Then there exists a [[Continuous function (topology)|continuous]] [[choice function|selection]] <math>f\colon X \to Y</math> of ...

...ph L. Walsh]] in 1929, using results proved by [[Henri Lebesgue|Lebesgue]] in 1907.<ref>{{cite journal|author=Walsh, J. L.|title=Über die Entwicklung ein ...ly]] on <math>\partial{K}</math> by (real-valued) [[harmonic polynomial]]s in the real variables {{math|x}} and {{math|y}}.<ref>{{cite book|author=Gameli ...

...the construction of a strictly convex [[compact space|compact]] [[surface (topology)|surface]] ''S'' whose [[Gaussian curvature]] is specified.<ref>{{cite jour ...re ''S''^n-1 to be the surface area measure of a [[convex body]] in <math>\mathbb{R}^n</math>. Here the surface area measure ''S_K'' ...

.../davis.12/book%20reviews/Gramlich-review-mybook.pdf|title=The geometry and topology of Coxeter groups review}}</ref> and ''Multiaxial Actions on Manifolds''. H ...atics at the same institution under the supervision of [[Wu-Chung Hsiang]] in 1975<ref>{{MathGenealogy|id=12021|title=Michael Walter Davis}}</ref> with a ...

In [[geometry]], the '''tennis ball theorem''' states that any [[smooth curve] ...Segre]], and the tennis ball theorem itself is a special case of a theorem in a 1977 paper by Joel L. Weiner.{{r|segre|global}} The name of the theorem c ...

...sciencedirect.com/science/article/pii/000187087190020X |journal=[[Advances in Mathematics]] |language=en |volume=6 |issue=3 |pages=329–346 |doi=10.1016/0 ...)|neighbourhoods]] <math>U_1</math> and <math>U_2</math> of <math>X</math> in <math>M</math>; ...

...1963) is a German mathematician, specializing in differential geometry and topology. ...ate=2016-01-19 }} in the ''A community of scholars'' list of the IAS</ref> In 2012 he was elected a Fellow of the [[American Mathematical Society]]. ...

...one can find a family of [[vector field]]s satisfying a certain [[Ordinary differential equation|ODE]]. ...<math>\{ \alpha_t \}_{t \in [0,1]}</math> and produce an entire [[Isotopy (topology)|isotopy]] <math>\psi_t</math> such that <math>\psi_t^* \alpha_t = \alpha_0 ...

...dian mathematician, specializing in [[symplectic geometry]] and symplectic topology. ...uébec à Montréal]] where he became a full professor (professeur titulaire) in 1991, after six years.<ref name="CV">{{cite web |title=C. V. — François Lal ...