AN IRREDUCIBLE HEEGAARD DIAGRAM OF THE REAL PROJECTIVE 3-SPACE P3 YOUNG HO IM and SOO
نویسندگان
چکیده
We give a genus 3 Heegaard diagram H of the real projective space P3, which has no waves and pairs of complementary handles. So Negami’s result that every genus 2 Heegaard diagram of P3 is reducible cannot be extended to Heegaard diagrams of P3 with genus 3.
منابع مشابه
A note on irreducible Heegaard diagrams
We construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different to that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducibl...
متن کاملPseudo Ricci symmetric real hypersurfaces of a complex projective space
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
متن کاملA 3-manifold complexity via immersed surfaces
We define an invariant, which we call surface-complexity, of closed 3manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on P-irreducible manifolds. Moreover, for P-irreducible manifolds, it equals the ...
متن کاملCritical Heegaard Surfaces
In this paper we introduce critical surfaces, which are described via a 1-complex whose definition is reminiscent of the curve complex. Our main result is that if the minimal genus common stabilization of a pair of strongly irreducible Heegaard splittings of a 3-manifold is not critical, then the manifold contains an incompressible surface. Conversely, we also show that if a nonHaken 3-manifold...
متن کاملDifferential Geometry of Real Hypersurfaces in Hermitian Symmetric Spaces with Rank 2 Jürgen Berndt and Young
In this talk, first we introduce the classification of homogeneous hypersurfaces in some Hermitian symmetric spaces of rank 1 or rank 2. In particular, we give a full expression of the geometric structures for hypersurfaces in complex two-plane Grassmannians G2(C) or in complex hyperbolic twoplane Grassmannians G2(C). Next by using the isometric Reeb flow we give a complete classification for h...
متن کامل