ALGEBRAIC AND SPECTRAL TORSIONS ON THE ALMOST COMMUTATIVE GEOMETRY OF DOUBLED MANIFOLDS

Speaker(s)

SUGATO MUKHOPADHYAY

Affiliation

SISSA, Trieste, Italy

Language of the talk

English

Date

Oct. 23, 2024, 5:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09

Information about the event

ZOOM

Seminar

North Atlantic Noncommutative Geometry Seminar

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I will present a construction of a noncommutative second order differential calculus on the algebra of smooth functions on the product of a manifold with the two-point space. This involves a modification of the standard Connes calculus on a spectral triple by following a recent work by Mesland and Rennie. I will compute the algebraic torsion of the product of the Levi-Civita connection on the manifold with an arbitrary connection on the two-point space, and find it to be generically not zero. Recently, Dąbrowski, Sitarz and Zalecki proposed a notion of the spectral-torsion functional on finitely summable spectral triples. We show that there exists a unique connection for our noncommutative differential calculus for which the algebraic torsion is compatible with the spectral-torsion functional. This talk is based on ongoing work with Ludwik Dąbrowski and Yang Liu.

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