TY  - JOUR
A1  - Roos, Saskia
A1  - Otoba, Nobuhiko
T1  - Scalar curvature and the multiconformal class of a direct product Riemannian manifold
JF  - Geometriae dedicata
N2  - For a closed, connected direct product Riemannian manifold (M, g) = (M-1, g(1)) x ... x (M-l, g(l)), we define its multiconformal class [[g]] as the totality {integral(2)(1)g(1) circle plus center dot center dot center dot integral(2)(l)g(l)} of all Riemannian metrics obtained from multiplying the metric gi of each factor Mi by a positive function fi on the total space M. A multiconformal class [[ g]] contains not only all warped product type deformations of g but also the whole conformal class [(g) over tilde] of every (g) over tilde is an element of[[ g]]. In this article, we prove that [[g]] contains a metric of positive scalar curvature if and only if the conformal class of some factor (Mi, gi) does, under the technical assumption dim M-i = 2. We also show that, even in the case where every factor (M-i, g(i)) has positive scalar curvature, [[g]] contains a metric of scalar curvature constantly equal to -1 and with arbitrarily large volume, provided l = 2 and dim M = 3.
KW  - Positive scalar curvature
KW  - Constant scalar curvature
KW  - The Yamabe
KW  - problem
KW  - Warped product
KW  - Umbilic product
KW  - Twisted product
Y1  - 2021
U6  - https://doi.org/10.1007/s10711-021-00636-9
SN  - 0046-5755
SN  - 1572-9168
VL  - 214
IS  - 1
SP  - 801
EP  - 829
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Ludewig, Matthias
A1  - Roos, Saskia
T1  - The chiral anomaly of the free fermion in functorial field theory
JF  - Annales Henri Poincaré : a journal of theoretical and mathematical physics
N2  - When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.
Y1  - 2020
U6  - https://doi.org/10.1007/s00023-020-00893-6
SN  - 1424-0637
SN  - 1424-0661
VL  - 21
IS  - 4
SP  - 1191
EP  - 1233
PB  - Springer International Publishing AG
CY  - Cham (ZG)
ER  - 
TY  - JOUR
A1  - Roos, Saskia
T1  - The Dirac operator under collapse to a smooth limit space
JF  - Annals of global analysis and geometry
N2  - Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.
KW  - Collapse
KW  - Dirac operator
KW  - Spin geometry
Y1  - 2019
U6  - https://doi.org/10.1007/s10455-019-09691-8
SN  - 0232-704X
SN  - 1572-9060
VL  - 57
IS  - 1
SP  - 121
EP  - 151
PB  - Springer
CY  - Dordrecht
ER  -