scholarly journals Critical metrics on connected sums of Einstein four-manifolds

2016 ◽  
Vol 292 ◽  
pp. 210-315 ◽  
Author(s):  
Matthew J. Gursky ◽  
Jeff A. Viaclovsky
Keyword(s):  
Critical Metrics ◽  
Connected Sums ◽  
Four 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.

Stable cohomotopy Seiberg–Witten invariants of connected sums of four-manifolds with positive first Betti number, I: Non-vanishing theorem

2015 ◽  
Vol 26 (06) ◽  
pp. 1541004 ◽  
Author(s):  
Masashi Ishida ◽  
Hirofumi Sasahira
Keyword(s):  
Betti Number ◽  
Witten Invariant ◽  
Vanishing Theorem ◽  
Connected Sums ◽  
Four Manifolds ◽  
Stable Cohomotopy ◽  
Invent Math

We shall prove a new non-vanishing theorem for the stable cohomotopy Seiberg–Witten invariant [S. Bauer and M. Furuta, Stable cohomotopy refinement of Seiberg–Witten invariants: I, Invent. Math.155 (2004) 1–19; S. Bauer, Stable cohomotopy refinement of Seiberg–Witten invariants: II, Invent. Math.155 (2004) 21–40.] of connected sums of 4-manifolds with positive first Betti number.

Quasipositive Links and Connected Sums

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

Export Citation Format

Share Document