The $\hatΓ$-genus and a regularization of an $S^1$-equivariant Euler class

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169575We show that a new multiplicative genus, in the sense of Hirzebruch, can be obtained by generalizing a calculation due to Atiyah and Witten. We introduce this as the $\hatΓ$-genus, compute its value for some examples and highlight some of its interesting properties. We also indicate a connection with the study of multiple zeta values, which gives an algebraic interpretation for our proposed regularization procedure.14 pages; version to appear in J. Phys. AMathematical Physics57R20 (Primary) 40A20, 55P35, 58J20 (Secondary)The $\hatΓ$-genus and a regularization of an $S^1$-equivariant Euler classtext