The problem of Lagrangian knots in four-manifolds

1996 ◽  
pp. 313-327 ◽  
Keyword(s):  
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.

scholarly journals On Einstein four-manifolds with S 1-actions

2004 ◽  
Vol 247 (3) ◽  
Author(s):  
Harish Seshadri
Keyword(s):  
Four Manifolds

Quantum fluctuations of the metric, three-geometries and conformal embeddings in four-manifolds

2021 ◽  
Author(s):  
Simon Davis
Keyword(s):  
Path Integrals ◽  
Invariance Group ◽  
Two Dimensional ◽  
Four Dimensions ◽  
Physical Conditions ◽  
Exponential Expansion ◽  
Cotangent Bundles ◽  
Four Manifolds ◽  
Conformal Embeddings ◽  
Natural Relation

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of [Formula: see text], which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be [Formula: see text], [Formula: see text] and [Formula: see text] with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

scholarly journals A note on positive-definite, symplectic four-manifolds

2018 ◽  
Vol 21 (1) ◽  
pp. 257-270 ◽  
Author(s):  
Jennifer Hom ◽  
Tye Lidman
Keyword(s):  
Positive Definite ◽  
Four Manifolds

scholarly journals A topological lagrangian for monopoles on four-manifolds

1995 ◽  
Vol 351 (1-3) ◽  
pp. 146-152 ◽  
Author(s):  
J.M.F. Labastida ◽  
M. Mariño
Keyword(s):  
Four Manifolds

scholarly journals Symmetry groups of four-manifolds

Topology ◽  
2002 ◽  
Vol 41 (4) ◽  
pp. 835-851 ◽  
Author(s):  
Michael P. McCooey
Keyword(s):  
Symmetry Groups ◽  
Four Manifolds

scholarly journals Computing trisections of 4-manifolds

2018 ◽  
Vol 115 (43) ◽  
pp. 10901-10907 ◽  
Author(s):  
Mark Bell ◽  
Joel Hass ◽  
Joachim Hyam Rubinstein ◽  
Stephan Tillmann
Keyword(s):  
Complexity Bounds ◽  
Four Manifolds

We describe an algorithm to compute trisections of orientable four-manifolds using arbitrary triangulations as input. This results in explicit complexity bounds for the trisection genus of a 4-manifold in terms of the number of pentachora (4-simplices) in a triangulation.

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