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...undle)|connection]] on a [[Hermitian vector bundle]] <math>E</math> over a smooth manifold <math>M</math> which is compatible with the [[Hermitian metric]] for all smooth vector fields <math>v</math> and all smooth sections <math>s,t</math> of <math>E</math>. ...

...ies of vector spaces to smoothly parameterized families of vector spaces. Smooth functors may therefore be uniquely extended to functors defined on [[vector ...harvnb|Kriegl|Michor|1997|p=290}}. {{harvnb|Lee|2002}}, pp.122–23 defines smooth functors over a different category, whose morphisms are [[linear isomorphis ...

...) = x</math>.<ref name ="Lee_1988">{{citation|title=Introduction to Smooth Manifolds|volume=218|series=Graduate Texts in Mathematics|first=John|last=Lee|publish [[Category:Manifolds]] ...

...] that cannot be expressed as a non-trivial [[connected sum]] of two ''n''-manifolds. Non-trivial means that neither of the two is an [[n-sphere|''n''-sphere]]. ...nected sum of a unique ([[up to]] [[homeomorphism]]) collection of prime 3-manifolds. ...

...perbundles and principal superconnections straightforwardly follow that of smooth [[principal bundle]]s and [[connection (principal bundle)|principal connect ...

...cation in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. ...rst=D. |last=Handron |title=Generalized billiard paths and Morse theory on manifolds with corners |journal=Topology and Its Applications |volume=126 |issue=1 |p ...

...topology of the 4-manifolds, including information on the existence of a [[smooth structure]]. ...osed manifold|closed]] 4-manifold ([[PL manifold|PL]] or [[smooth manifold|smooth]]). ...

{{Short description|Geometric structure on a smooth manifold}} ...lmost-contact structure''' is a certain kind of geometric structure on a [[smooth manifold]]. Such structures were introduced by [[Shigeo Sasaki]] in 1960. ...

{{Short description|Result about foliation of compact 3-manifolds}} Theorem: ''A smooth codimension-one foliation of the [[3-sphere]]'' ''S''³ ''has a c ...

...Binghamton]] with thesis ''Orbit maps of local <math>S^1</math>-actions on manifolds of dimension less than five '' under the supervision of Louis McAuley.<ref> His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with ...

...ll-behaved]] functions cannot have certain kinds of well-behaved invariant manifolds. ...h> cannot have a 1-dimensional [[compact space|compact]] [[smooth function|smooth]] [[invariant manifold]]. In particular, such a map cannot have a [[homocl ...

...|doi=10.1090/gsm/020|mr=1707327}}</ref><ref>A.Scorpan, The wild world of 4-manifolds (p.90), AMS Pub. {{isbn|0-8218-3749-4}}</ref> ...rst2=Rostislav| last2=Matveyev| title=A convex decomposition theorem for 4-manifolds|journal= [[International Mathematics Research Notices]] |year=1998|volume=1 ...

...s there are various types of manifolds, there are various types of maps of manifolds. ...DIFF]], the category of [[piecewise]]-smooth maps between piecewise-smooth manifolds. ...

...ve algebras]]. However, graded manifolds are characterized by sheaves on [[smooth manifold]]s, while supermanifolds are constructed by gluing of sheaves of [ ==Graded manifolds== ...

...=Blair|first1=David E.|title=Riemannian geometry of contact and symplectic manifolds|edition=Second edition of 2002 original|series=Progress in Mathematics|volu ...l|first1=Katsuei|last1=Kenmotsu|title=A class of almost contact Riemannian manifolds|journal=[[Tohoku Mathematical Journal]]|series=Second Series|volume=24|year ...

...s a problem concerning the realisation of [[homology class]]es by singular manifolds.<ref>{{Cite journal|last=Eilenberg|first=Samuel|authorlink=Samuel Eilenberg All elements of <math>H_k(X)</math> are realisable by smooth manifolds provided <math>k\le 6</math>. Moreover, any cycle can be realized by the m ...

...manifold]]s, this means that the embedding of <math>A</math> must also be smooth. ...

== Smooth mappings == ...ame{Map}(M, N)</math> that consists of all the <math> \mathcal{C}^r</math>-smooth maps from <math>M</math> to <math>N</math>. It can be equipped with the wea ...

...o a [[collar neighbourdhood]].<ref>{{citation|title=Introduction to Smooth Manifolds|volume=218|series=Graduate Texts in Mathematics|first=John|last=Lee|publish [[Category:Manifolds]] ...

{{Short description|Topologies defined on the set of smooth mappings between manifolds}} ...ition|topologies]] defined on the set of [[smooth mapping]]s between two [[smooth manifold]]s. They are named after the American mathematician [[Hassler Whit ...