Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism cl...Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.展开更多
It is an important problem in topology to verify whether two embeddings are isotopic.This work proposes an algorithm for computing Haefliger-Wu invariants for isotopy based on algebraic topological methods.Given a sim...It is an important problem in topology to verify whether two embeddings are isotopic.This work proposes an algorithm for computing Haefliger-Wu invariants for isotopy based on algebraic topological methods.Given a simplicial complex embedded in the Euclidean space,the deleted product of it is the direct product with diagonal removed.The Gauss map transforms the deleted product to the unit sphere.The pull-back of the generator of the cohomology group of the sphere defines characteristic class of the isotopy of the embedding.By using Mayer Vietoris sequence and Ku¨nneth theorem,the computational algorithm can be greatly simplified.The authors prove the ranks of homology groups of the deleted product of a closed surface and give explicit construction of the generators of the homology groups of the deleted product.Numerical experimental results show the efficiency and efficacy of the proposed method.展开更多
We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a...We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward.A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.展开更多
基金Supported by NSFC(11371118)SRFDP(20121303110004)+1 种基金HNSF(A2011205075)HNUHH(20110403)
文摘Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.
基金the Science Challenge Project of China(TZZT2019-B1)the National Natural Science Foundation of China under Grant Nos.61720106005+1 种基金6177210561936002。
文摘It is an important problem in topology to verify whether two embeddings are isotopic.This work proposes an algorithm for computing Haefliger-Wu invariants for isotopy based on algebraic topological methods.Given a simplicial complex embedded in the Euclidean space,the deleted product of it is the direct product with diagonal removed.The Gauss map transforms the deleted product to the unit sphere.The pull-back of the generator of the cohomology group of the sphere defines characteristic class of the isotopy of the embedding.By using Mayer Vietoris sequence and Ku¨nneth theorem,the computational algorithm can be greatly simplified.The authors prove the ranks of homology groups of the deleted product of a closed surface and give explicit construction of the generators of the homology groups of the deleted product.Numerical experimental results show the efficiency and efficacy of the proposed method.
文摘We propose a conjecture on the relative twist formula of l-adic sheaves,which can be viewed as a generalization of Kato-Saito’s conjecture.We verify this conjecture under some transversal assumptions.We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward.A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.
