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A Nonconnecting Delooping of Algebraic KTheory
"... Given a ring R, it is known that the topological space BGl(R) + is an infinite loop space. One way to construct an infinite loop structure is to consider the category F of free Rmodules, or rather its classifying space BF, as food for suitable infinite loop space machines. These machines produce co ..."
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Cited by 30 (3 self)
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Given a ring R, it is known that the topological space BGl(R) + is an infinite loop space. One way to construct an infinite loop structure is to consider the category F of free Rmodules, or rather its classifying space BF, as food for suitable infinite loop space machines. These machines produce connective spectra whose zeroth space is (BF Z × BGl(R) +. In this paper we consider categories C (F) = F, C (F),... of parameterized =1 = = =1 = free modules and bounded homomorphisms and show that the spaces (BC) =0 + = (BF)
Uniqueness theorems for certain triangulated categories possessing an Adams spectral sequence
, 139
"... 1.2. The axioms ..."
The loop space of the Qconstruction
 Illinois J. Math
, 1987
"... The higher algebraic Kgroups are defined as gi.// [ ’lri+ lQ’I rl Q’I for an exact category J/. We present a simplicial set Gt ’ with the property that a’l is naturally homotopy equivalent to the loop space IQ’I, and thus Kilt ’ %1G’I. In this way we given an algebraic description of the loop space ..."
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Cited by 20 (7 self)
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The higher algebraic Kgroups are defined as gi.// [ ’lri+ lQ’I rl Q’I for an exact category J/. We present a simplicial set Gt ’ with the property that a’l is naturally homotopy equivalent to the loop space IQ’I, and thus Kilt ’ %1G’I. In this way we given an algebraic description of the loop space, which a priori, has no such description. The case where t ’ is a category in which all the exact sequences split was
Noncommutative Localization And Chain Complexes I. Algebraic K And LTheory
, 2001
"... The noncommutative (Cohn) localization # 1 R of a ring R is defined for any collection # of morphisms of f.g. projective left Rmodules. We exhibit # 1 R as the endomorphism ring of R in an appropriate triangulated category. We use this expression to prove that if Tor 1 then every bounded f. ..."
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Cited by 6 (1 self)
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The noncommutative (Cohn) localization # 1 R of a ring R is defined for any collection # of morphisms of f.g. projective left Rmodules. We exhibit # 1 R as the endomorphism ring of R in an appropriate triangulated category. We use this expression to prove that if Tor 1 then every bounded f.g.
Identifying assembly maps in K and Ltheory
 MATHEMATISCHE ANNALEN
, 2004
"... In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K and Ltheory, and C∗theory. ..."
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Cited by 3 (0 self)
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In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K and Ltheory, and C∗theory.