Simplicial methods and the interpretation of “triple” cohomology

1975 ◽  
Vol 3 (163) ◽  
pp. 0-0 ◽  
Author(s):  
J. Duskin
Keyword(s):  
Simplicial Methods

Solving Implicit ODEs by Simplicial Methods

1991 ◽  
pp. 193-196
Author(s):  
Sergio de Freitas ◽  
Geovan Tavares
Keyword(s):  
Simplicial Methods

Simplicial methods for quadratic programming

1964 ◽  
Vol 11 (3-4) ◽  
pp. 273-302 ◽  
Author(s):  
C. van de Panne ◽  
Andrew Whinston
Keyword(s):  
Quadratic Programming ◽  
Simplicial Methods

scholarly journals CROSSED MODULE BUNDLE GERBES; CLASSIFICATION, STRING GROUP AND DIFFERENTIAL GEOMETRY

2011 ◽  
Vol 08 (05) ◽  
pp. 1079-1095 ◽  
Author(s):  
BRANISLAV JURČO
Keyword(s):  
Differential Geometry ◽  
Geometric Realization ◽  
Equivalence Classes ◽  
Point Of View ◽  
Crossed Module ◽  
Simplicial Group ◽  
Stable Equivalence ◽  
Bundle Gerbe ◽  
Bundle Gerbes ◽  
Simplicial Methods

We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to a (Lie) crossed module (H → D) there is a simplicial group [Formula: see text], the nerve of the groupoid [Formula: see text] defined by the crossed module, and its geometric realization, the topological group [Formula: see text]. We introduce crossed module bundle gerbes so that their (stable) equivalence classes are in a bijection with equivalence classes of principal [Formula: see text]-bundles. We discuss the string group and string structures from this point of view. Also, we give a simplicial interpretation to the bundle gerbe connection and bundle gerbe B-field.

scholarly journals Simplicial homotopy theory, link homology and Khovanov homology

2018 ◽  
Vol 27 (07) ◽  
pp. 1841002
Author(s):  
Louis H. Kauffman
Keyword(s):  
Homotopy Theory ◽  
Khovanov Homology ◽  
Frobenius Algebra ◽  
Link Diagram ◽  
Link Homology ◽  
Simplicial Homotopy ◽  
Simplicial Methods

This paper shows how, in principle, simplicial methods, including the well-known Dold–Kan construction can be applied to convert link homology theories into homotopy theories. The paper studies particularly the case of Khovanov homology and shows how simplicial structures are implicit in the construction of the Khovanov complex from a link diagram and how the homology of the Khovanov category, with coefficients in an appropriate Frobenius algebra, is related to Khovanov homology. This Khovanov category leads to simplicial groups satisfying the Kan condition that are relevant to a homotopy theory for Khovanov homology.

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