On the Connected Sum of Projective Planes, Tori, and Klein Bottles

1971 ◽  
Vol 78 (2) ◽  
pp. 185-187
Author(s):  
J. C. Alexander
Keyword(s):  
Projective Planes ◽  
Connected Sum

scholarly journals Four-manifolds up to connected sum with complex projective planes

2022 ◽  
Vol 144 (1) ◽  
pp. 75-118
Author(s):  
Daniel Kasprowski ◽  
Mark Powell ◽  
Peter Teichner
Keyword(s):  
Projective Planes ◽  
Connected Sum ◽  
Four Manifolds ◽  
Complex Projective

On knotted real projective planes

2015 ◽  
Vol 24 (10) ◽  
pp. 1540011
Author(s):  
Yongju Bae ◽  
Seonmi Choi ◽  
Akio Kawauchi
Keyword(s):  
Projective Planes ◽  
Connected Sum ◽  
The Relationship

Let [Formula: see text] be a hyperbolic transformation. Let B be a new band attaching to L such that [Formula: see text] is also a hyperbolic transformation. In this paper, we will study the relationship between the realizing surfaces [Formula: see text] and [Formula: see text]. If B is a noncoherent band to both L and [Formula: see text] such that [Formula: see text] is defined, then [Formula: see text] and [Formula: see text] are ambient isotopic, where RP2 is one of the standard real projective planes. We will study the triviality of [Formula: see text] because as an application, RP2 can untangle some knotted sphere [Formula: see text] with suitable conditions, when it is attached to [Formula: see text] by the connected sum.

Rewriting systems for the surface classification theorem

2010 ◽  
Vol 20 (4) ◽  
pp. 577-588
Author(s):  
GABRIELE PULCINI
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Classification Theorem ◽  
Alternative Proof ◽  
Connected Sum ◽  
Rewriting Systems ◽  
Surface Classification ◽  
Orientable Surfaces ◽  
Computational Properties ◽  
Standard Word

The work reported in this paper refers to Massey's proof of the surface classification theorem based on the standard word-rewriting treatment of surfaces. We arrange this approach into a formal rewriting systemand provide a new version of Massey's argument. Moreover, we study the computational properties of two subsystems of:orfor dealing with words denoting orientable surfaces andnorfor dealing with words denoting non-orientable surfaces. We show how such properties induce an alternative proof for the surface classification in which the basic homeomorphism between the connected sum of three projective planes and the connected sum of a torus with a projective plane is not required.

Spiky projective planes

1991 ◽  
Vol 257 (1-2) ◽  
pp. 51-55
Author(s):  
D. Johnston
Keyword(s):  
Projective Planes
Sign in / Sign up

Export Citation Format

Share Document