'GROUP-COMPLETION', LOCAL COEFFICIENT SYSTEMS AND PERFECTION

2013 ◽  
Vol 64 (3) ◽  
pp. 795-803 ◽  
Author(s):  
O. Randal-Williams



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.



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


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


1943 ◽  
Vol 46 (320) ◽  
pp. 754-755
Author(s):  
Kiyosi YAMAGATA ◽  
Kenjiro SIRAKAWA


1998 ◽  
Vol 08 (02) ◽  
pp. 141-152 ◽  
Author(s):  
N. D. Gilbert

We consider properties of a 2-complex associated by Squier to a monoid presentation. We show that the fundamental groupoid admits a monoid structure, and we establish a relationship between its group completion and the fundamental group of the 2-complex. We also treat a modified complex, due to Pride, for monoid presentations of groups, and compute the structure of the fundamental groupoid in this setting.



1990 ◽  
Vol 115 (3-4) ◽  
pp. 359-365 ◽  
Author(s):  
John W. Rutter

SynopsisThe generalised Whitney sum (fibre-join) and the h-fibre-join can be defined in topM, the category of spaces over M. We note here some general properties of these constructions, and, as a specific example, we consider the relation between them and the extensions to the topM category of the top h-fibre-sequences F∗ΩB→E ∪ CF→B determined by top fibrations F→E→B. As an application we obtain the truncated local coefficient cohomology sequence for a top fibration which is topM principal fibration: this situation applies, for example, to the various stages of the Postnikov decomposition of a non-simply connected space X, and in this case we have M = K1(π1(X)).



2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Byron E. Moutafis ◽  
Christos K. Filelis-Papadopoulos ◽  
George A. Gravvanis

During the last decades, the continuous expansion of supercomputing infrastructures necessitates the design of scalable and robust parallel numerical methods for solving large sparse linear systems. A new approach for the additive projection parallel preconditioned iterative method based on semiaggregation and a subspace compression technique, for general sparse linear systems, is presented. The subspace compression technique utilizes a subdomain adjacency matrix and breadth first search to discover and aggregate subdomains to limit the average size of the local linear systems, resulting in reduced memory requirements. The depth of aggregation is controlled by a user defined parameter. The local coefficient matrices use the aggregates computed during the formation of the subdomain adjacency matrix in order to avoid recomputation and improve performance. Moreover, the rows and columns corresponding to the newly formed aggregates are ordered last to further reduce fill-in during the factorization of the local coefficient matrices. Furthermore, the method is based on nonoverlapping domain decomposition in conjunction with algebraic graph partitioning techniques for separating the subdomains. Finally, the applicability and implementation issues are discussed and numerical results along with comparative results are presented.



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