On the construction of codimension two minimal immersions of exotic spheres into euclidean spheres. II

1987 ◽  
Vol 195 (3) ◽  
pp. 301-313 ◽  
Author(s):  
Wu-teh Hsiang ◽  
Wu-yi Hsiang
Keyword(s):  
Codimension Two ◽  
Minimal Immersions ◽  
Euclidean Spheres ◽  
Exotic Spheres

On the construction of codimension two minimal immersions of exotic spheres into Euclidean spheres

1985 ◽  
Vol 82 (3) ◽  
pp. 447-460 ◽  
Author(s):  
Wu -teh Hsiang ◽  
Wu -yi Hsiang ◽  
Ivan Sterling
Keyword(s):  
Codimension Two ◽  
Minimal Immersions ◽  
Euclidean Spheres ◽  
Exotic Spheres

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 The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

Zero singularities of codimension two in a delayed predator-prey diffusion system

2017 ◽  
Vol 227 ◽  
pp. 10-17 ◽  
Author(s):  
Jinling Wang ◽  
Jinling Liang ◽  
Yurong Liu ◽  
Jin-Liang Wang
Keyword(s):  
Diffusion System ◽  
Predator Prey ◽  
Codimension Two

scholarly journals Thin Schubert cells of codimension two

2008 ◽  
Vol 48 (2) ◽  
pp. 265-275
Author(s):  
Shinsuke Odagiri
Keyword(s):  
Codimension Two
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