Oriented Cohomology Theories of Algebraic Varieties

This article contains proofs of the results announced by Panin and Smirnov (http://www. math.uiuc.edu/k-theory/0459/2000) in the part concerning general properties of oriented cohomology theories of algebraic varieties. It is constructed one-to-one correspondences between orientations, Chern structures and Thom structures on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.     

On the Buchstaber Subring in MS p

A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.     

Crumpled laminations and manifolds of nonfinite type

Using a group-theoretic construction due to Bestvina and Brady, we build -manifolds which admit partitions into closed, connected -manifolds but which do not have finite homotopy type.

     

上协边类纤维丛表示的若干性质

本文研究了底空间为实射影空间时上协边类纤维丛表示的若干性质．     

All frame-spun knots are slice

Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of . We show that all frame-spun knots are slice (null-cobordant).

     

单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类. 利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数, 推广了现有文献中的相关结果.     

The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus of knots. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant for this inequality.     

Semi-invariants in surgery

A semi-invariant in surgery is an invariant of a quadratic Poincaré complex which is defined in terms of a null-cobordism. We define five such gadgets: the semicharacteristic, the semitorsion, the cross semitorsion, the torsion semicharacteristic, and the cross torsion semicharacteristic. We describe applications to the evaluation of surgery obstructions, especially in the odd-dimensional case.     

不动点集为RP(4)∪ P(4,2n-1)的对合

设(M,T)是一个光滑闭流形上的对合,不动点集为F=RP(4)UP(4,2n-1),则它的每一个对合(M,T)必协边(RP(4)×RP(4),twist)和(P(4,2n),T')之一.     

-actions with

Suppose that is a smooth -action on a closed smooth -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set vanish in positive dimension. This paper shows that if 2^k\dim F$"> and each -dimensional part possesses the linear independence property, then bounds equivariantly, and in particular, is the best possible upper bound of if is nonbounding.