Homology fibrations and the ?group-completion? theorem

1976 ◽  
Vol 31 (3) ◽  
pp. 279-284 ◽  
Author(s):  
D. McDuff ◽  
G. Segal



1980 ◽  
Vol 3 (1) ◽  
pp. 105-116
Author(s):  
Bruno Courcelle ◽  
Jean-Claude Raoult

We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations.



10.37236/2929 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Jürgen Bierbrauer ◽  
Klaus Metsch

Consider the symmetric group $S_n$ with the Hamming metric. A  permutation code on $n$ symbols is a subset $C\subseteq S_n.$ If $C$ has minimum distance $\geq n-1,$ then $\vert C\vert\leq n^2-n.$ Equality can be reached if and only if a projective plane of order $n$ exists. Call $C$ embeddable if it is contained in a permutation code of minimum distance $n-1$ and cardinality $n^2-n.$ Let $\delta =\delta (C)=n^2-n-\vert C\vert$ be the deficiency of the permutation code $C\subseteq S_n$ of minimum distance $\geq n-1.$We prove that $C$ is embeddable if either $\delta\leq 2$ or if $(\delta^2-1)(\delta +1)^2<27(n+2)/16.$ The main part of the proof is an adaptation of the method used to obtain the famous Bruck completion theorem for mutually orthogonal latin squares.



1990 ◽  
Author(s):  
Janice H. Schopler ◽  
Maeda J. Galinsky
Keyword(s):  




Author(s):  
Marco Schlichting

We prove the analog for the $K$ -theory of forms of the $Q=+$ theorem in algebraic $K$ -theory. That is, we show that the $K$ -theory of forms defined in terms of an $S_{\bullet }$ -construction is a group completion of the category of quadratic spaces for form categories in which all admissible exact sequences split. This applies for instance to quadratic and hermitian forms defined with respect to a form parameter.



2011 ◽  
Vol 54 (2) ◽  
pp. 515-529
Author(s):  
Philip G. Spain

AbstractPalmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra.When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.



2004 ◽  
Vol 17 (9) ◽  
pp. 798-806 ◽  
Author(s):  
Alexei L. Polishchuk ◽  
Kevin L. Bartlett ◽  
Lee A. Friedman ◽  
Maitland Jones


2012 ◽  
Vol 12 (4) ◽  
pp. 1925-1940 ◽  
Author(s):  
Anssi Lahtinen
Keyword(s):  
K Theory ◽  


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