The $\mathbf{P}^1$-motivic Gysin map

Longke Tang

The $\mathbf{P}^1$-motivic Gysin map

Algebraic Geometry 2026-04-29 v1 Algebraic Topology K-Theory and Homology

Authors: Longke Tang

Abstract

We develop a $\mathbf{P}^1$ -unstable non- $\mathbf{A}^1$ -invariant theory of motivic spaces and spectra, and construct the Gysin map therein for regular immersions. This in particular gives the Gysin map in the Annala--Hoyois--Iwasa $\mathbf{P}^1$ -motivic spectra, and thus gives a uniform construction for the Gysin maps of various cohomology theories.

Keywords

motives thurston maps harmonic maps

Cite

@article{arxiv.2604.24888,
  title  = {The $\mathbf{P}^1$-motivic Gysin map},
  author = {Longke Tang},
  journal= {arXiv preprint arXiv:2604.24888},
  year   = {2026}
}

Comments

40 pages

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