scholarly journals Matrix factorizations and link homology II

2008 ◽  
Vol 12 (3) ◽  
pp. 1387-1425 ◽  
Author(s):  
Mikhail Khovanov ◽  
Lev Rozansky
Keyword(s):  
Matrix Factorizations ◽  
Link Homology

scholarly journals Matrix factorizations and link homology

2008 ◽  
Vol 199 (1) ◽  
pp. 1-91 ◽  
Author(s):  
Mikhail Khovanov ◽  
Lev Rozansky
Keyword(s):  
Matrix Factorizations ◽  
Link Homology

scholarly journals A note on Khovanov–Rozansky sl2-homology and ordinary Khovanov homology

2014 ◽  
Vol 23 (12) ◽  
pp. 1450057 ◽  
Author(s):  
Mark C. Hughes
Keyword(s):  
Khovanov Homology ◽  
Matrix Factorizations ◽  
Link Homology ◽  
Virtual Links ◽  
Made In

In this paper we present an explicit isomorphism between Khovanov–Rozansky sl2-homology and ordinary Khovanov homology. This result was originally claimed in Khovanov and Rozansky's paper [Matrix factorizations and link homology, Fund. Math.199(1) (2008) 1–91, MR 2391017 (2010a:57011)], though the proof was never presented. The main missing detail is providing a coherent choice of signs when identifying variables in the sl2-homology. Along with the behavior of the signs and local orientations in the sl2-homology, both theories behave differently when we try to extend their definitions to virtual links, which seemed to suggest that the sl2-homology may instead correspond to a different variant of Khovanov homology. In this paper we describe both theories and prove that they are in fact isomorphic by showing that a coherent choice of signs can be made. In doing so we emphasize the interpretation of the sl2-complex as a cube of resolutions.

scholarly journals Rigorous Perturbation Bounds of Some Matrix Factorizations

2010 ◽  
Vol 31 (5) ◽  
pp. 2841-2859 ◽  
Author(s):  
X.-W. Chang ◽  
D. Stehlé
Keyword(s):  
Matrix Factorizations ◽  
Perturbation Bounds

Input Matrix Factorizations for Constrained Control Allocation

2018 ◽  
Vol 63 (4) ◽  
pp. 1163-1170 ◽  
Author(s):  
Martin Kirchengast ◽  
Martin Steinberger ◽  
Martin Horn
Keyword(s):  
Matrix Factorizations ◽  
Control Allocation ◽  
Constrained Control ◽  
Input Matrix

scholarly journals Matrix factorizations for domestic triangle singularities

2015 ◽  
Vol 140 (2) ◽  
pp. 239-278
Author(s):  
Dawid Edmund Kędzierski ◽  
Helmut Lenzing ◽  
Hagen Meltzer
Keyword(s):  
Matrix Factorizations
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