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Ronghui Ji 《K-Theory》1995,9(1):59-76
For certain classes of discrete groups we verify the idempotent conjectures for various group algebras by the method of cyclic cohomology. In particular, the Banach 1 (G) of a torsion free word hyperbolic groupG of Gromov contains no nontrivial idempotents. Moreover, the range of any tracial state onK
0(1(G)) is .Sponsored in part by a grant from the National Science Foundation. 相似文献
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Kenny Pruitt 《International Journal of Mathematical Education in Science & Technology》2018,49(6):944-947
The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings. 相似文献
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Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6. 相似文献
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In Thomassen (1995) [4], Thomassen proved that planar graphs of girth at least 5 are 3-choosable. In Li (2009) [3], Li improved Thomassen’s result by proving that planar graphs of girth 4 with no 4-cycle sharing a vertex with another 4- or 5-cycle are 3-choosable. In this paper, we prove that planar graphs of girth 4 with no 4-cycle sharing an edge with another 4- or 5-cycle are 3-choosable. It is clear that our result strengthens Li’s result. 相似文献
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A graph G is edge-L-colorable, if for a given edge assignment L={L(e):e∈E(G)}, there exists a proper edge-coloring ? of G such that ?(e)∈L(e) for all e∈E(G). If G is edge-L-colorable for every edge assignment L with |L(e)|≥k for e∈E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph with maximum degree Δ(G)≠5 and without adjacent 3-cycles, or with maximum degree Δ(G)≠5,6 and without 7-cycles, then G is edge-(Δ(G)+1)-choosable. 相似文献
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In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. Among other things, we prove that a complete noncompact Kahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1(M)^2 is biholomorphic to C2. 相似文献
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A graph G is k-choosable if every vertex of G can be properly colored whenever every vertex has a list of at least k available colors. Grötzsch’s theorem [4] states that every planar triangle-free graph is 3-colorable. However, Voigt [M. Voigt, A not 3-choosable planar graph without 3-cycles, Discrete Math. 146 (1995) 325-328] gave an example of such a graph that is not 3-choosable, thus Grötzsch’s theorem does not generalize naturally to choosability. We prove that every planar triangle-free graph without 7- and 8-cycles is 3-choosable. 相似文献