---
abstract: 'We establish the analogue of the Friedlander-Mazur conjecture for Teh’s reduced Lawson homology groups of real varieties, which says that the reduced Lawson homology of a real quasi-projective variety $X$ vanishes in homological degrees larger than the dimension of $X$ in all weights. As an application we obtain a vanishing of homotopy groups of the mod-2 topological groups of averaged cycles and a characterization in a range of indices of the motivic cohomology of a real variety as homotopy groups of the complex of averaged equidimensional cycles. We also establish an equivariant Poincare duality between equivariant Friedlander-Walker real morphic cohomology and dos Santos’ real Lawson homology. We use this together with an equivariant extension of the mod-2 Beilinson-Lichtenbaum conjecture to compute some real Lawson homology groups in terms of Bredon cohomology.'
author:
- Jeremiah Heller
- Mircea Voineagu
bibliography:
- 'remreal.bib'
title: Vanishing Theorems for Real Algebraic Cycles
---

Introduction
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Let $X$ be a quasi-projective real variety. The Galois group $G = Gal(\C/\R)$ acts on $\mcal{Z}_{q}(X_{\C})$, the topological group of $q$-cycles on the complexification. Cycles on the real variety $X$ correspond to cycles on $X_{\C}$ which are fixed by conjugation. Inside the topological group of $\mcal{Z}_{q}(X_{\C})^{G}$ of 