On the homotopy theory of $\mathbf{G}$ - spaces

Amit Sharma

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arXiv · 1512.03698

On the homotopy theory of $\mathbf{G}$ - spaces

Amit Sharma

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Abstract

The aim of this paper is to show that the most elementary homotopy theory of $\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are presented as Relative categories. We establish the equivalence by constructing a strict homotopy equivalence between the two relative categories. No Model category structure is assumed on either Relative Category.

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Amit Sharma. 2015-12-11. On the homotopy theory of $\mathbf{G}$ - spaces. https://arxiv.org/abs/1512.03698

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