scholarly journals A homotopy+ solution to the A-B slice problem

2017 ◽  
Vol 26 (02) ◽  
pp. 1740018
Author(s):  
Michael Freedman ◽  
Vyacheslav Krushkal
Keyword(s):  
Free Groups ◽  
Homotopy Formula ◽  
Link Homotopy

The A-B slice problem, a reformulation of the four-dimensional topological surgery conjecture for free groups, is shown to admit a link-homotopy[Formula: see text] solution. The proof relies on geometric applications of the group-theoretic [Formula: see text]-Engel relation. Implications for the surgery conjecture are discussed.

Sulphoamidic Phtalocyaninic Pigments and Dyes(II)

2008 ◽  
Vol 59 (5) ◽  
Author(s):  
Elena Stingaciu ◽  
Corneliu Minca ◽  
Ion Sebe
Keyword(s):  
Ir Spectra ◽  
Aromatic Amines ◽  
Free Groups ◽  
Cyanuric Chloride ◽  
Layer Chromatography ◽  
Phenylene Diamine

This work concerns the synthesis of pigments and phtalocyanine dyes obtained through the sulphonation of copper phtalocyanine and amidation with some aliphatic and aromatic amines (lauryl-amine, i-propyl-amine, hexadecyl-amine, stearyl-amine and acetyl-p-phenylene-diamine) with good properties for the electrotechnic utilisation and for toner materials. The pigments with amino free groups are transformed by condensation with cyanuric chloride in phtalocyanine pigments with different tinctorial properties. The dyes were analyzed through the layer chromatography and were characterized on the IR spectra bases and tinctorial tests.

Generating the inverse limit of free groups

2021 ◽  
Vol 578 ◽  
pp. 371-401
Author(s):  
Gregory R. Conner ◽  
Wolfgang Herfort ◽  
Curtis A. Kent ◽  
Petar Pavešić
Keyword(s):  
Inverse Limit ◽  
Free Groups

scholarly journals Cyclic-Homology Chern–Weil Theory for Families of Principal Coactions

2020 ◽  
Author(s):  
Piotr M. Hajac ◽  
Tomasz Maszczyk
Keyword(s):  
Cyclic Homology ◽  
Quantum Deformation ◽  
Homotopy Formula ◽  
Standard Quantum ◽  
Unital Algebra ◽  
Hopf Fibrations ◽  
Chain Homotopy ◽  
Cartan Model ◽  
Extension Algebra ◽  
Hochschild Complex

AbstractViewing the space of cotraces in the structural coalgebra of a principal coaction as a noncommutative counterpart of the classical Cartan model, we construct the cyclic-homology Chern–Weil homomorphism. To realize the thus constructed Chern–Weil homomorphism as a Cartan model of the homomorphism tautologically induced by the classifying map on cohomology, we replace the unital subalgebra of coaction-invariants by its natural H-unital nilpotent extension (row extension). Although the row-extension algebra provides a drastically different model of the cyclic object, we prove that, for any row extension of any unital algebra over a commutative ring, the row-extension Hochschild complex and the usual Hochschild complex are chain homotopy equivalent. It is the discovery of an explicit homotopy formula that allows us to improve the homological quasi-isomorphism arguments of Loday and Wodzicki. We work with families of principal coactions, and instantiate our noncommutative Chern–Weil theory by computing the cotrace space and analyzing a dimension-drop-like effect in the spirit of Feng and Tsygan for the quantum-deformation family of the standard quantum Hopf fibrations.

scholarly journals Minimal partition-free groups

2021 ◽  
Author(s):  
Afsane Bahri ◽  
Zeinab Akhlaghi ◽  
Behrooz Khosravi
Keyword(s):  
Free Groups

scholarly journals Freely indecomposable almost free groups with free abelianization

2020 ◽  
Vol 23 (3) ◽  
pp. 531-543
Author(s):  
Samuel M. Corson
Keyword(s):  
Free Groups ◽  
Uncountable Cardinals

AbstractFor certain uncountable cardinals κ, we produce a group of cardinality κ which is freely indecomposable, strongly κ-free, and whose abelianization is free abelian of rank κ. The construction takes place in Gödel’s constructible universe L. This strengthens an earlier result of Eklof and Mekler.

scholarly journals Products of free groups in Lie groups

2021 ◽  
Author(s):  
Caterina Campagnolo ◽  
Holger Kammeyer
Keyword(s):  
Lie Groups ◽  
Free Groups

scholarly journals On the structure of some contranormal-free groups

2021 ◽  
pp. 1-7
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Free Groups

scholarly journals On the graded quotients of the rings of Fricke characters of free groups

2015 ◽  
Vol 430 ◽  
pp. 94-118 ◽  
Author(s):  
Eri Hatakenaka ◽  
Takao Satoh
Keyword(s):  
Free Groups
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