caa a22 4500 388046503 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199808 xx s 000 0 eng 10.1017/S1446788700039446 doi S1446788700039446 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700039446 The Vanishing problem of the string class with degree 3 [Elektronische Daten] Let ξbe an SO(n)-bundle over a simple connected manifold M with a spin structure Q → M. The string class is an obstruction to h1 the structure group LSpin(n) of the loop group bundle LQ → LM to the universal central extension of LSpain(n) by the circle. We prove that the string class vanishes if and only if 1/2 the first Pontrjagin clsss of values when M is a compact simply connected homogeneous space of rank one, a simpiy connected 4 dimensional manifold or a finite product space of those manifolds. This result is deduced by using the Eclesberg spectral sequence converging to the mod p cohomology of LM whose E2-term to the Hochschild homology of the mod p cohomology algebra of M. The key to the consideration is existence of a morphism of algebras, which is injective below degree 3, from an important graded commutator algebra into the Hochschild homology of a certain graded commutative algebra. Copyright © Australian Mathematical Society 1998 primary 57R20 nationallicence secondary 55P35 nationallicence 57T35 nationallicence Kuribayashi Katsuhiko Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700, Japan e-mail: kuri@geom.xmath.ous.ac.jp Yamaguchi Toshihiro Graduate School of Science and Technology, Okayama University, Okayama 700, Japan e-mail: t_ yama@math.okayama-u.ac.jp Journal of the Australian Mathematical Society Cambridge University Press 65/1(1998-08), 129-142 1446-7887 65:1<129 1998 65 JAZ https://doi.org/10.1017/S1446788700039446 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700039446 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kuribayashi Katsuhiko Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700, Japan e-mail: kuri@geom.xmath.ous.ac.jp NATIONALLICENCE 700 1- Yamaguchi Toshihiro Graduate School of Science and Technology, Okayama University, Okayama 700, Japan e-mail: t_ yama@math.okayama-u.ac.jp NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/1(1998-08), 129-142 1446-7887 65:1<129 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge