scholarly journals On 2-knots and connected sums with projective planes

2019 ◽  
Vol 207 (1) ◽  
pp. 23-27
Author(s):  
Vincent Longo
Keyword(s):  
Projective Planes ◽  
Connected Sums

Quasipositive Links and Connected Sums

2020 ◽  
Vol 54 (1) ◽  
pp. 64-67
Author(s):  
S. Yu. Orevkov
Keyword(s):  
Connected Sums

Constructing symplectic manifolds

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Final Section ◽  
Symplectic Manifolds ◽  
Homotopy Equivalence ◽  
Codimension Two ◽  
Open Manifolds ◽  
Connected Sums ◽  
Symplectic Forms ◽  
Ambient Manifold ◽  
Blowing Up ◽  
Four Manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

Spiky projective planes

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

scholarly journals On submaximal curves in fake projective planes

2021 ◽  
Vol 225 (10) ◽  
pp. 106709
Author(s):  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Planes

4-Dimensional projective planes of Lenz type III

1972 ◽  
Vol 1 (1) ◽  
Author(s):  
Helmut Salzmann
Keyword(s):  
Projective Planes ◽  
Type Iii

scholarly journals Maximal arcs in projective planes of order 16 and related designs

2019 ◽  
Vol 19 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Mustafa Gezek ◽  
Vladimir D. Tonchev ◽  
Tim Wagner
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Maximal Arcs ◽  
Even Order

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal (52,4)-arcs, as well as some newly discovered maximal (52,4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(120,8,1) design associated with a maximal (120,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose–Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52,4,1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.

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