arXiv subjects

Dennis Nguyen

Publications and source records attributed to Dennis Nguyen.

2 recordsLinked to original sources

arXiv2024

Cobordism Obstructions to Complex Sections II: Torsion Obstructions

In the previous paper, we studied obstructions to the existence of complex sections on almost complex manifolds up to cobordism. We determined the obstruction rationally, in terms of the Chern classes. In this paper, we study the torsion obstructions, that is, the obstructions which vanish after tensoring with $\mathbb{Q}$ or multiplication by an integer. Calculations with the Adams-Novikov spectral sequence for the Thom spectra $\mathbf{MTU}(d)$ allow us to show the torsion obstructions for low $r$. For prime $p\geq 3$, we show that torsion obstructions for finding $r$ complex sections of order $p$ vanish for $r<p^2-p$.

math.AT↗

arXiv2023

Cobordism Obstructions to Complex Sections

A notion of vector field cobordism for oriented manifolds was defined by B\"okstedt and Svane. We extend this notion to define complex section cobordism for almost complex manifolds. We then determine the complex section cobordism groups and a relevant cobordism category. We describe an obstruction which tells us when a cobordism class contains a manifold, which can be equipped with $r$ linearly independent complex sections, in terms of the Chern classes. Finally, we show that this obstruction vanishes for certain multiplicative generators in the complex cobordism ring.

math.AT↗