Connected sums of compact manifolds and homogeneity

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

Author(s):  
Dusa McDuff ◽  
Dietmar Salamon

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.


2007 ◽  
Vol 233 (2) ◽  
pp. 404-416 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera

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