TY  - JOUR
A1  - Bär, Christian
A1  - Mazzeo, Rafe
T1  - Manifolds with many Rarita-Schwinger fields
JF  - Communications in mathematical physics
N2  - The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
Y1  - 2021
U6  - https://doi.org/10.1007/s00220-021-04030-0
SN  - 0010-3616
SN  - 1432-0916
VL  - 384
IS  - 1
SP  - 533
EP  - 548
PB  - Springer
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Bär, Christian
T1  - The Faddeev-LeVerrier algorithm and the Pfaffian
JF  - Linear algebra and its applications
N2  - We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.
KW  - Characteristic polynomial
KW  - Determinant
KW  - Pfaffian
KW  - Gauss-Bonnet-Chern
KW  - theorem
Y1  - 2021
U6  - https://doi.org/10.1016/j.laa.2021.07.023
SN  - 0024-3795
SN  - 1873-1856
VL  - 630
SP  - 39
EP  - 55
PB  - Elsevier
CY  - New York
ER  -