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Differential operators and the Witten genus for projective spaces and Milnor manifolds

Published online by Cambridge University Press:  26 June 2003

IMMA GÁLVEZ  and
ANDREW TONKS
IMMA GÁLVEZ
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH. e-mail: [email protected]
ANDREW TONKS
Affiliation:
Department of Computing, Communications Technology and Mathematics, London Metropolitan University, London N7 8DB. e-mail: [email protected]
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Abstract

A $genus$ (in the sense of Hirzebruch [4]) is a multiplicative invariant of cobordism classes of manifolds. Classical examples include the numerical invariants given by the signature and the $\widehat{A}$- and Todd genera. More recently genera were introduced which take as values modular forms on the upper half-plane, $\frak{h}=\{\,\tau\;|\;\mathrm{Im}(\tau)>0\,\}$. The main examples are the elliptic genus $\phi_{ell}$ and the Witten genus $\phi_W$; we refer the reader to the texts [7] or [9] for details.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 1 , July 2003 , pp. 123 - 131
Copyright
2003 Cambridge Philosophical Society

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Footnotes

Partially supported by DGES grant BFM2001-2031.