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Homotopical intersection theory I
We give a new approach to intersection theory. Our “cycles” are closed manifolds mapping into compact manifolds and our “intersections” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [H-Q], but our proofs are fundamentally di...
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متن کاملOn cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
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The independent assignment problem (or the weighted matroid intersection problem) is extended using Dress-Wenzel’s matroid valuations, which are attached to the vertex set of the underlying bipartite graph as an additional weighting. Specifically, the problem considered is: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectiv...
متن کاملon cycles in intersection graphs of rings
let $r$ be a commutative ring with non-zero identity. we describe all $c_3$- and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. also, we shall describe all complete, regular and $n$-claw-free intersection graphs. finally, we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1896
ISSN: 1802-114X
DOI: 10.21136/cpmf.1896.123316