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...nt union of manifolds. The ring is [[graded ring|graded]] by dimensions of manifolds and is denoted by where <math>\Omega^{SO}_n</math> consists of oriented cobordism classes of manifolds of dimension ''n''. One can also define an '''unoriented cobordism ring''', ...

...pdf/82435349.pdf |journal=[[Topology (journal)|Topology]] |volume=4 |issue=3 |pages=283–293 |doi=10.1016/0040-9383(65)90012-1|mr=0187250 }}</ref> [[Category:Manifolds]] ...

...cation in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. ...fied Morse theory |publisher=Springer |orig-date=1988 |date=2012 |isbn=978-3-642-71714-7 |url={{GBurl|Cxv-CAAAQBAJ|pg=PR9}} }} [http://www.math.ias.edu/ ...

...books.google.com/books?id=TASWAwAAQBAJ | title=The Geometric Topology of 3-manifolds | isbn=9780821810408 | last1=Bing | first1=R. H. | date=31 December 1983 }} ...

...lzant polytope is the moment polytope of such a manifold, and any two such manifolds with equivalent moment polytopes (up to translations and <math>GL(n,\mathb |issue=3 ...

...] 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]]. A 3-manifold is irreducible if and only if it is prime, except for two cases: t ...

...MA|year=2010|mr=2682326|isbn=978-0-8176-4958-6|doi=10.1007/978-0-8176-4959-3|zbl=1246.53001}} ...l|first1=Katsuei|last1=Kenmotsu|title=A class of almost contact Riemannian manifolds|journal=[[Tohoku Mathematical Journal]]|series=Second Series|volume=24|year ...

...S/Park City Math. Ser.|year=2009|volume=15|chapter=Hyperbolic geometry and 3-manifold topology|pages=73–103|mr=2503493|isbn=978-0-8218-4766-4}} ...ournal)|Topology]]|issn=0040-9383|volume=13|pages=267–273|mr=0353317|issue=3|doi-access=}} ...

...meomorphic to a product of two odd-dimensional spheres of dimension ≥&nbsp;3. ...is simply connected (in dimension 2, all simply connected compact complex manifolds are Kähler). ...

...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 ...

...ly, non Kählerian nearly Kähler manifolds are called "strict nearly Kähler manifolds". Nearly Kähler manifolds, also known as almost Tachibana manifolds, were studied by Shun-ichi Tachibana in 1959<ref> ...

...as. [[Graded manifold]]s are characterized by sheaves on [[manifold|smooth manifolds]], while [[supermanifold]]s are constructed by gluing of sheaves of [[super | isbn = 981-02-1228-3 ...

...olds |journal=Differential Geometry and Its Applications |volume=18 |issue=3 |pages=239–253|doi=10.1016/S0926-2245(02)00160-2 }}</ref> A manifold <math> ''Clifford structures'' are fundamental in studying Osserman manifolds. An [[Riemann curvature tensor|algebraic curvature tensor]] <math>R</math> ...

These manifolds are important in both [[Morse theory]] and [[foliation|foliation theory]]: | title = Manifolds which are like projective planes ...

...t|thumb|An annulus is an orientable I-bundle. This example is embedded in 3-space with an even number of twists|200px]] ...nal spaces. These observations are simple well known facts on elementary [[3-manifold]]s. ...

{{Short description|Way to create new manifolds out of disk bundles}} ...ame=":0" /> and subsequently used extensively in surgery theory to produce manifolds and [[normal invariant|normal map]]s with given [[surgery obstruction]]s. ...

...concept which helps to answer the question whether two homotopy equivalent manifolds are [[diffeomorphic]] (or [[Piecewise linear manifold|PL-homeomorphic]] or ...We call two homotopy equivalences <math>f_i: M_i \to X</math> from closed manifolds <math>M_i</math> of dimension <math>n</math> to <math>X</math> (<math>i=0,1 ...

...010. xvi+343 pp. {{ISBN|978-0-8176-4958-6}}, {{doi|10.1007/978-0-8176-4959-3}} {{closed access}} ...saki |first1=Shigeo |journal=Tohoku Mathematical Journal |volume=12 |issue=3|pages=459–476|doi-access=free }} ...

....ed.ac.uk/~aar/papers/milncycl.pdf|publisher=Conference on the Topology of Manifolds. Vol. 13. 1968.|accessdate=25 August 2017}}</ref> ...

{{Short description|Result about foliation of compact 3-manifolds}} : ''A codimension-one [[foliation]] of a compact 3-manifold whose [[universal covering space]] is not contractible must have a ...