Categorical shadows lurking behind integral formulas for genera

Domenico Fiorenza (Università degli Studi di Roma "La Sapienza")

18-Nov-2021, 13:30-14:30 (2 years ago)

Abstract: Professor Friedrich: And so, if you have a complex genus taking rational values, i.e., a ring homomorphism from the complex cobordism ring to the field Q of rational numbers, you have an integral formula expressing it.

The Categorist: If a formula is true, it must be expressed by a commutative diagram.

Professor Friedrich: But my formula is true!

The Categorist: Then it must be expressed by a commutative diagram.

Professor Friedrich: Show me.

The Categorist: Let us consider the category of spectra…

Professor Friedrich: And so?

The Categorist: Well… I don’t see a commutative diagram here.

Professor Friedrich: And so?

The Categorist: And so your formula must be false.

Professor Friedrich: But my formula is true!

The Categorist: Impossible.

Sir Michael: There is something I think I know on the Spanier-Whitehead dual of a smooth manifold that may happen to be of some relevance here.

(Emil Ionesco, Triceratops)

category theory

Audience: researchers in the topic


ItaCa Fest 2021

Series comments: ItaCa Fest is an online webinar aimed to gather the community of ItaCa.

Organizer: Progetto ItaCa*
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