## Geometry Seminar - Abstracts

### Talk

Tuesday 3 September 2024, 16:00 - 17:00 in HG03.085

**Ahina Nandy** (RU)

*Some Remarks on the Special Linear Algebraic Cobordism \(\mathrm{MSL}\)*

### Abstract

In classical topology, different cobordism theories can be thought of as universal cohomology theories with certain orientations. For example, complex cobordism (\(\mathrm{MU}\)) is the universal complex oriented cohomology theory; that is cohomology theories with Thom isomorphism for every complex vector bundle. Special unitary cobordism (\(\mathrm{MSU}\)) has the universal property among theories with Thom isomorphism for \(\mathrm{SU}\)-torsors. The analogous notion of different notions of orientations is very well studied in \(\mathbb{A}^1\)-homotopy theory. I will introduce these notions. I will mostly talk about special linear orientation, and special linear algebraic cobordism \(\mathrm{MSL}\). This can be thought of as an analogue of the classical theory \(\mathrm{MSU}\). I will draw some parallel between \(\mathrm{MSU}\), and \(\mathrm{MSL}\). If time permits, I will introduce "metalinear" orientation, which is ubiquitous in \(\mathbb{A}^1\)-homotopy theory. I will also report on joint work in progress (with T. Brazelton) about "metalinear cobordism".

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