The Defect of Codimension-Two Submanifolds of Homotopy Complex Projective Space

1990 ◽  
Vol s2-41 (3) ◽  
pp. 565-576
Author(s):  
Robert D. Little
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Codimension Two ◽  
Complex Projective ◽  
Homotopy Complex

On the first pontrjagin class of homotopy complex projective spaces

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Yasuhiko Kitada
Keyword(s):  
Projective Space ◽  
Smooth Manifold ◽  
Complex Projective Space ◽  
Projective Spaces ◽  
Homotopy Equivalent ◽  
Complex Projective Spaces ◽  
Pontrjagin Class ◽  
Complex Projective ◽  
Homotopy Complex

AbstractLet M 2n be a closed smooth manifold homotopy equivalent to the complex projective space ℂP(n). It is known that the first Pontrjagin class p 1(M) of M 2n has the form (n+1+24α(M))u 2 for some integer α(M) where u is a generator of H 2(M; ℤ). We prove that α(M) is even when n is even but not divisible by 64.

scholarly journals Regular cyclic actions on complex projective space with codimension-two fixed points

1998 ◽  
Vol 65 (1) ◽  
pp. 51-67 ◽  
Author(s):  
Robert D. Little
Keyword(s):  
Fixed Point ◽  
Projective Space ◽  
Fixed Points ◽  
Cyclic Group ◽  
Complex Projective Space ◽  
Fixed Point Set ◽  
Codimension Two ◽  
Point Set ◽  
Isolated Point ◽  
Complex Projective

AbstractIfM2nis a cohomologyCPnandPis an odd prime, letGpbe the cyclic group of orderp. A TypeI I0Gpaction onM2nis an action with fixed point set a codimension-2 submanifold and an isolated point. A TypeI I0Gpaction is standard if it is regular and the degree of the fixed codimension-2 submanifold is one. If n is odd and M2nadmits a standardGpaction of TypeI I0, then every TypeI I0GpactionM2nis standard and so, if n is odd,CPnadmits aGpaction of TypeI I0if and only if the action is standard.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Sign in / Sign up

Export Citation Format

Share Document