# Questions tagged [cotangent-bundles]

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I've seen hints at the following result: Let $M$ be a 3-dimensional manifold and let $T := T^*M$ be the cotangent bundle. By Schur-Weyl Duality, the 3rd tensor product can be written as follows: $$T^... 0answers 65 views ### On the degrees of the normal and tangent sheaves of Gorenstein curves in Pn It is known that if an irreducible curve C is a local complete intersection in \mathbb{P}^n, then \wedge^{n-1}\mathcal{N}\otimes\omega_{\mathbb{P}^n} is isomomorphic to the dualizing sheaf \... 0answers 122 views ### Restriction of the sheaf of relative differentials Let f:X\rightarrow C be a morphism, where C is a smooth curve, and let \Omega_f be the sheaf of relative differentials. For t\in C let i_t:X_t = f^{-1}(t)\rightarrow X be the inclusion of ... 0answers 301 views ### Beyond smoothness-the clear picture about the notion of a differential form In this paper N.Teleman constructs the signature operator on an arbitrary (closed, oriented) Lipschitz manifold with coefficients in a vector bundle \xi. In particular the notion of a differential ... 0answers 117 views ### how to understand the manifold with boundary jet bundle and cotangent bundle with boundary Suppose that M\subset (W^{2n},\omega) is an n-dimensional manifold with smooth boundary \partial M, where (W,\omega) is a 2n-dimensional Kähler manifold and boundary with contact type ... 0answers 110 views ### Is there a precisely formulable obstruction for the tangent bundle being a Lie algebra bundle? Although vector fields (which are sections of the tangent bundle) form Lie algebras, the bundle itself, as far as I know, almost never carries Lie algebra structure; that is, in general, I believe, ... 0answers 139 views ### Lagrangian up to Hamiltonian in cotangent bundle I want to understand the folklore conjecture that, in a CY manifold, Lagrangians up to Hamiltonian isotopies are represented by special Lagrangians by examining cotangent bundle and Hodge theory. ... 1answer 208 views ### Natural extension homomorphism and wrong-way maps in K-theory Let X \subset Y be two smooth manifolds. To the inclusion I:X \to Y corresponds the so called wrong-way map in K-theory i_!:K(X) \to K(Y). It is constructed as follows: to the inclusion X \... 3answers 813 views ### Splitting of tangent bundle Is it possible to give an example of n dimensional manifold with the property that the tangent bundle TM cannot be expressed as Whitney sum of two subbundles? It is certain true for two sphere; it ... 0answers 212 views ### Reference for plumbing cotangent bundles as Liouville manifolds A Liouville domain (W, \omega,\alpha, X) is a compact manifold W with boundary \partial W, and a exact symplectic structure \omega = d\alpha, \iota_X \omega = \alpha, such that X points ... 1answer 513 views ### Are the Sasaki metrics on tangent and cotangent bundle isomorphic? Let (M,g) be a Riemannian manifold. Then there is the well-known Sasaki metric that makes (TM,\hat{g}) a Riemannian manifold. In a similar way, one can construct a Sasaki metric \bar{g} on the ... 1answer 915 views ### characteristic classes of homotopy equivalent manifolds Let M,N be two manifolds of different dimensions. Suppose M\simeq N, i.e. M is homotopy equivalent to N. Do the Stiefel-Whitney classes of the tangent bundles of M and N equal$$ w(TM)=w(...
Let $X$ be a manifold and $T^\ast X$ the cotangent bundle. Let $\alpha$ denote the tautological $1$-form on $T^\ast X$ so that $(T^\ast X, \omega=-d\alpha)$ is a symplectic manifold. I want to know ...