Cobordism of symplectic manifolds and asymptotic expansions
نویسندگان
چکیده
The cobordism ring B∗ of symplectic manifolds defined by V. L. Ginzburg is isomorphic to the Pontrjagin ring of complex-oriented manifolds with free circle actions. This provides an interpretation of the formal group law of complex cobordism as a composition-law on certain asymptotic expansions. An appendix discusses some related questions about toric manifolds.
منابع مشابه
Asymptotic expansion of 1-dimensional sub-manifolds of stable and unstable manifolds in a 4-dimensional symplectic mapping
We analytically compute asymptotic expansions of a 1-dimensional submanifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us to capture exponentially small splitting of separatrices and also to obtain explicit functional approximations of the sub-manifolds. In addition, we show the ...
متن کاملGeometric cobordism categories
In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex structures along with a holomorphic map to a target complex manifold. A general notion of “geometric structure” is defined using sheaf theoretic constructions. Our m...
متن کاملOn Symplectic Cobordisms
In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has in nitely many concave symplectic llings and that all overtwisted contact 3-manifolds are \symplectic cobordism equivalent".
متن کاملTHE SIGNATURE OF SYMPLECTIC MANIFOLDS 255 Class Name w ¡ E 77 ' ( BO ; Z / 2 Z ) Stiefel - Whitney
The motivation for this work was a calculation by Oshanin of the image of the signature homomorphism from the special unitary cobordism ring into the integers. Here we compute this image for symplectic cobordism. This is accomplished by proving two divisibility theorems and then giving examples to show the theorems are the best possible.
متن کاملMathematische Zeitschrift Bordism of semi-free S1-actions
We calculate geometric and homotopical bordism rings associated to semi-free S1 actions on complex manifolds, giving explicit generators for the geometric theory. The classification of semi-free actions with isolated fixed points up to cobordism complements similar results from symplectic geometry.
متن کامل