Čech and Steenrod Homotopy Theories with Applications to Geometric Topology

1976 ◽  
Author(s):  
David A. Edwards ◽  
Harold M. Hastings
Keyword(s):  
Geometric Topology

scholarly journals Cross-sections of unknotted ribbon disks and algebraic curves

2019 ◽  
Vol 155 (2) ◽  
pp. 413-423
Author(s):  
Kyle Hayden
Keyword(s):  
Cross Sections ◽  
Algebraic Curves ◽  
American Mathematical Society ◽  
Geometric Topology ◽  
Mathematical Society ◽  
Advanced Mathematics ◽  
Low Dimensional Topology ◽  
Low Dimensional ◽  
Holomorphic Disks

We resolve parts (A) and (B) of Problem 1.100 from Kirby’s list [Problems in low-dimensional topology, in Geometric topology, AMS/IP Studies in Advanced Mathematics, vol. 2 (American Mathematical Society, Providence, RI, 1997), 35–473] by showing that many nontrivial links arise as cross-sections of unknotted holomorphic disks in the four-ball. The techniques can be used to produce unknotted ribbon surfaces with prescribed cross-sections, including unknotted Lagrangian disks with nontrivial cross-sections.

Geometric Topology: Recent Developments

1991 ◽  
Author(s):  
Jeff Cheeger ◽  
Mikhail Gromov ◽  
Christian Okonek ◽  
Pierre Pansu
Keyword(s):  
Geometric Topology ◽  
Recent Developments

scholarly journals K-Theory and Geometric Topology

2005 ◽  
pp. 577-610
Author(s):  
Jonathan Rosenberg
Keyword(s):  
Geometric Topology ◽  
K Theory

The minimum deformation retract on the wormhole spacetime

2020 ◽  
Vol 17 (13) ◽  
pp. 2050198
Author(s):  
M. Abu-Saleem
Keyword(s):  
Line Element ◽  
Geometric Topology ◽  
Deformation Retract ◽  
Lagrangian Equations ◽  
Minimum Deformation

In this paper, we investigate the topology of a wormhole from the viewpoint of the theory of retracting and var-folding. We deduce the equatorial geodesics on the line element of the wormhole and discuss the minimum deformation retract related to this space. Using the Lagrangian equations we find that there is a type of minimum retraction of a wormhole with associated topology. We also extend the result to the [Formula: see text]-dimensional wormhole and show that the end limit of var-folding is 0-dimensional wormhole and obtain the relation between limit var-folding and limit retraction. We find a new application in geometric topology and astrophysics.

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