Open Manifolds of Nonnegative Curvature

2009 ◽  
pp. 109-134
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

Complete open manifolds of nonnegative curvature

1974 ◽  
Vol 15 (1) ◽  
pp. 126-136 ◽  
Author(s):  
V. A. Sharafutdinov
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

Volume growth of open manifolds with nonnegative curvature

1990 ◽  
Vol 8 (2) ◽  
pp. 159-165
Author(s):  
Viktor Schroeder ◽  
Martin Strake
Keyword(s):  
Volume Growth ◽  
Nonnegative Curvature ◽  
Open Manifolds

Open manifolds of nonnegative curvature

1991 ◽  
Vol 55 (6) ◽  
pp. 2115-2130
Author(s):  
V. B. Marenich ◽  
V. A. Toponogov
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

scholarly journals The holonomy in open manifolds of nonnegative curvature.

1996 ◽  
Vol 43 (2) ◽  
pp. 263-272 ◽  
Author(s):  
Valery Marenich
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

scholarly journals Open manifolds with asymptotically nonnegative curvature

2005 ◽  
Vol 49 (3) ◽  
pp. 705-717
Author(s):  
Mahaman Bazanfaré
Keyword(s):  
Nonnegative Curvature ◽  
Open Manifolds

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.

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