SAMELSON PRODUCTS IN FUNCTION SPACES

Title & Authors
SAMELSON PRODUCTS IN FUNCTION SPACES
GATSINZI, JEAN-BAPTISTE; KWASHIRA, RUGARE;

Abstract
We study Samelson products on models of function spaces. Given a map $\small{f:X{\rightarrow}Y}$ between 1-connected spaces and its Quillen model $\small{{\mathbb{L}}(f):{\mathbb{L}}(V){\rightarrow}{\mathbb{L}}(W)}$, there is an isomorphism of graded vector spaces $\small{{\Theta}:H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W))){\rightarrow}H_*({\mathbb{L}}(W){\oplus}Der({\mathbb{L}}(V),{\mathbb{L}}(W)))}$. We define a Samelson product on $\small{H_*(Hom_{TV}(TV{\otimes}({\mathbb{Q}}{\oplus}sV),{\mathbb{L}}(W)))}$.
Keywords
Lie model;Lie algebra of derivations;Samelson product;
Language
English
Cited by
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