Year: 2013
Type: preprint
Abstract: Let $M$ be a connected, closed oriented manifold. Let $ω\in H^m(M)$ be its orientation class. Let $χ(M)$ be its Euler characteristic. Consider the free loop fibration $ΩM\buildrel{i}\over\hookrightarrow LM\buildrel{ev}\over\twoheadrightarrow M$. For any class $a\in H^*(LM)$ of positive degree, we prove that the cup product $χ(M)a\cup ev^*(ω)$ is null. In particular, if $i^*:H^*(LM;\mathbb{F}_p)\twoheadrightarrow H^*(ΩM;\mathbb{F}_p)$ is onto then $χ(M)$ is divisible by $p$ (or $M$ is a point).
Source: arXiv (Cornell University)
Author: Menichi, Luc
Institution: Laboratoire Angevin de Recherche en Mathématiques
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1522800010