Algebraic Hopf invariants and rational models for mapping spaces
| Autor: | Felix Wierstra |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Rational homotopy theory Coalgebra Homotopy 010102 general mathematics 01 natural sciences Combinatorics Morphism Number theory Mathematics::Category Theory 0103 physical sciences Homotopy Lie algebra FOS: Mathematics Algebraic Topology (math.AT) 010307 mathematical physics Geometry and Topology Mathematics - Algebraic Topology 0101 mathematics Algebraic number Invariant (mathematics) Mathematics |
| DOI: | 10.48550/arxiv.1612.07762 |
| Popis: | In this paper we will define an invariant $mc_{\infty}(f)$ of maps $f:X \rightarrow Y_{\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\mathbb{Q}}$. We prove that this invariant is complete, i.e. $mc_{\infty}(f)=mc_{\infty}(g)$ if an only if $f$ and $g$ are homotopic. We will also construct an $L_{\infty}$-model for the based mapping space $Map_*(X,Y_{\mathbb{Q}})$ from a $C_{\infty}$-coalgebra and an $L_{\infty}$-algebra. Comment: Improved certain sections of the paper, corrected some errors. 18 pages |
| Databáze: | OpenAIRE |
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