An algebraic loop theorem and the decomposition of PD 3 -pairs

2006 ◽  
Vol 39 (1) ◽  
pp. 46-52
Author(s):  
John Crisp
Keyword(s):  
Loop Theorem ◽  
Algebraic Loop

The equivariant Dehn's lemma and loop theorem

1981 ◽  
Vol 56 (1) ◽  
pp. 225-239 ◽  
Author(s):  
William H. Meeks ◽  
Shing-Tung Yau
Keyword(s):  
Loop Theorem

scholarly journals Torsion free actions on 1-acyclic manifolds and the loop theorem

Topology ◽  
1981 ◽  
Vol 20 (4) ◽  
pp. 353-363 ◽  
Author(s):  
Matthew G. Brin
Keyword(s):  
Loop Theorem ◽  
Free Actions ◽  
Torsion Free

scholarly journals Algebraic loop structures on algebra comultiplications

2019 ◽  
Vol 17 (1) ◽  
pp. 742-757 ◽  
Author(s):  
Dae-Woong Lee
Keyword(s):  
Lie Algebra ◽  
Rational Cohomology ◽  
Algebraic Loop

Abstract In this paper, we study the algebraic loop structures on the set of Lie algebra comultiplications. More specifically, we investigate the fundamental concepts of algebraic loop structures and the set of Lie algebra comultiplications which have inversive, power-associative and Moufang properties depending on the Lie algebra comultiplications up to all the possible quadratic and cubic Lie algebra comultiplications. We also apply those notions to the rational cohomology of Hopf spaces.

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