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- 저자 : Rugare Kwashira (검색결과 3 건)
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A NOTE ON DERIVATIONS OF A SULLIVAN MODEL
Kwashira, Rugare Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.
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SAMELSON PRODUCTS IN FUNCTION SPACES
GATSINZI, JEAN-BAPTISTE,KWASHIRA, RUGARE Korean Mathematical Society 2015 대한수학회보 Vol.52 No.4
We study Samelson products on models of function spaces. Given a map $f:X{\rightarrow}Y$ between 1-connected spaces and its Quillen model ${\mathbb{L}}(f):{\mathbb{L}}(V){\rightarrow}{\mathbb{L}}(W)$, there is an isomorphism of graded vector spaces ${\Theta}:H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W))){\rightarrow}H_*({\mathbb{L}}(W){\oplus}Der({\mathbb{L}}(V),{\mathbb{L}}(W)))$. We define a Samelson product on $H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W)))$.
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SAMELSON PRODUCTS IN FUNCTION SPACES
Jean-Baptiste Gatsinzi,Rugare Kwashira 대한수학회 2015 대한수학회보 Vol.52 No.4
We study Samelson products on models of function spaces. Given a map f : X → Y between 1-connected spaces and its Quillen model L(f) : L(V ) → L(W), there is an isomorphism of graded vector spaces θ : H∗(HomTV (TV ⊗ (Q ⊕ sV ), L(W))) → H∗(L(W) ⊕ Der(L(V ), L(W))). We define a Samelson product on H∗(HomTV (TV ⊗ (Q ⊕ sV ), L(W))).
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