A Congruence for the Signature of an Embedded Manifold
نویسندگان
چکیده
Let M " be a smooth, closed, orientable 2«-manifold and suppose that Kx"~ is an orientable submanifold of M " dual to a cohomology class x . If d is a positive integer, the signatures of Kd"~ and K"~ are related by a numerical congruence. If n is odd, then any codimension 2 submanifold of CP" fixed by a diffeomorphism of odd prime order is dual to the generator of the cohomology algebra.
منابع مشابه
Signature submanifolds for some equivalence problems
This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.
متن کاملبهبود مدل تفکیککننده منیفلدهای غیرخطی بهمنظور بازشناسی چهره با یک تصویر از هر فرد
Manifold learning is a dimension reduction method for extracting nonlinear structures of high-dimensional data. Many methods have been introduced for this purpose. Most of these methods usually extract a global manifold for data. However, in many real-world problems, there is not only one global manifold, but also additional information about the objects is shared by a large number of manifolds...
متن کاملMod-2 Equivalence of the K -theoretic Euler and Signature Classes
It is well-known that the Euler characteristic χ(M) and the signature Sign(M) of a closed oriented manifold M of dimension 4n are two integers of the same parity. This fact is an easy consequence of Poincaré duality and we briefly recall its proof. Let βk = dimHk(M ;R). By Poincaré duality, βk = β4n−k and there is a non-degenerate bilinear form (the “intersection form”) onH2n(M ;R). Let β + 2n ...
متن کاملEinstein structures on four-dimensional nutral Lie groups
When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...
متن کاملMod 3 congruence and twisted signature of 24 dimensional string manifolds
Let M be a 2n dimensional smooth closed oriented manifold. Let g be a Riemmian metric on TM and ∇ the associated Levi-Civita connection. Let V be a complex vector bundle over M with a Hermitian metric h and a unitary connection ∇ . Let ΛC(T ∗M) be the complexified exterior algebra bundle of TM and let 〈 , 〉ΛC(T∗M) be the Hermitian metric on ΛC(T ∗M) induced by g . Let dv be the Riemannian volum...
متن کامل