scholarly journals Path-connectedness of the moduli spaces of metrics with positive isotropic curvature on four-manifolds

2015 ◽  
Vol 366 (1-2) ◽  
pp. 819-851 ◽  
Author(s):  
Bing-Long Chen ◽  
Xian-Tao Huang
Keyword(s):  
Moduli Spaces ◽  
Isotropic Curvature ◽  
Path Connectedness ◽  
Four Manifolds ◽  
Spaces Of Metrics

Four-manifolds with positive isotropic curvature

2016 ◽  
Vol 11 (5) ◽  
pp. 1123-1149
Author(s):  
Bing-Long Chen ◽  
Xian-Tao Huang
Keyword(s):  
Isotropic Curvature ◽  
Four Manifolds

scholarly journals A PERTURBATION AND GENERIC SMOOTHNESS OF THE VAFA–WITTEN MODULI SPACES ON CLOSED SYMPLECTIC FOUR-MANIFOLDS

2018 ◽  
Vol 61 (2) ◽  
pp. 471-486 ◽  
Author(s):  
YUUJI TANAKA
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Smooth Manifold ◽  
Structure Group ◽  
Dimension Zero ◽  
Four Manifolds ◽  
Perturbation Parameters

AbstractWe prove a Freed–Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa–Witten equations on a closed symplectic four-manifold by using a method developed by Feehan for the study of the PU(2)-monopole equations on smooth closed four-manifolds. We introduce a set of perturbation terms to the Vafa–Witten equations, and prove that the moduli space of solutions to the perturbed Vafa–Witten equations on a closed symplectic four-manifold for the structure group SU(2) or SO(3) is a smooth manifold of dimension zero for a generic choice of the perturbation parameters.

scholarly journals ASD moduli spaces over four-manifolds with tree-like ends

2004 ◽  
Vol 8 (2) ◽  
pp. 779-830 ◽  
Author(s):  
Tsuyoshi Kato
Keyword(s):  
Moduli Spaces ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document