In this paper, we give the cobordism classes of the involution (M 3+k ,T).

Let(M,T)be an involution on a closed manifold,and let F denote the fixed psint set of (M,T),we determine the bordism classes of those involutions with fixed point set F=RP(1)×HP(n),HP(n) denoting the n dimensional quaternionic projective space.

In this paper,the bordism classes of the involutions with F=RP1(2m)∪RP2(2m)∪RP(3) are determined(m is a odd number).

The bordism classes of the involutions with ∪mi=1CP_i(2n+1) are investigated.

For a differentiable involution(M~r,T)on a closed manifold,if the fixed point set is P(1,n)×HP(1),where n is odd,then(M~r,T)bounds.

To show that for any differentiable involution on an 4n+2m+2K k-dimensional manifold(M,T)whose fixed point set F is Dold manifold P(2m,2n+1),with m evenly even,we have:if n≥m>0 then(M,T)bounds;if m>n≥0 and m minus n is even them(M,T)bounds.

Based on the methods of fast triangle-triangle overlap test using signed distances,a fast coincident intersection test algorithm for 3-D convex polygons based on clamping-edge pair is presented,which provides a coincident computational method for the overlap judgment between convex polygons and expands the algorithm application object.