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

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

2008-04-17

arxiv.org/abs/0804.2714v4

J. Phys. A: Math. Theor. 41 (2008) 425204

Physics

Mathematical Physics

14 pages; version to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/41/42/425204

We 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 $\hat{\Gamma}$-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.

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