# Quaternionic Projective Bundle Theorem and Gysin Triangle in MW-Motivic Cohomology

## TL;DR

This paper proves a splitting theorem for the motives of quaternionic Grassmannians and symplectic bundles within MW-motivic cohomology, extending classical results and establishing a Gysin triangle in this context.

## Contribution

It introduces a quaternionic projective bundle theorem in MW-motivic cohomology and constructs the Gysin triangle, advancing the understanding of MW-motives.

## Key findings

- Motives of quaternionic Grassmannians split in effective MW-motives
- Extension of the splitting to arbitrary symplectic bundles
- Establishment of the Gysin triangle in MW-motivic cohomology

## Abstract

In this paper, we show that the motive of the quaternionic Grassmannian $HP^n$ (as defined by I. Panin and C. Walter) splits in the category of effective MW-motives (as defined by B. Calm\`es, F. D\'eglise and J. Fasel). Moreover, we extend this result to an arbitrary symplectic bundle, obtaining the so-called quaternionic projective bundle theorem. Finally, we give the Gysin triangle in MW-motivic cohomology.