The Classical Dirac (Atiyah-Singer) Operators on Spin Manifolds

1993 ◽  
pp. 36-39
Author(s):  
Bernhelm Booß-Bavnbek ◽  
Krzysztof P. Wojciechowski
Keyword(s):  
Spin Manifolds

Gaussian dominance on compact spin manifolds

1984 ◽  
Vol 149 (1-3) ◽  
pp. 167-170 ◽  
Author(s):  
A. Patrascioiu ◽  
J.L. Richard
Keyword(s):  
Spin Manifolds ◽  
Gaussian Dominance

scholarly journals Tangent frame fields on spin manifolds

1978 ◽  
Vol 76 (1) ◽  
pp. 157-167 ◽  
Author(s):  
Duane Randall
Keyword(s):  
Spin Manifolds

Lorentzian structures of open, spin manifolds

1989 ◽  
Vol 30 (3) ◽  
pp. 619-623 ◽  
Author(s):  
Krystyna Bugajska
Keyword(s):  
Spin Manifolds

scholarly journals The Kernel of the Rarita–Schwinger Operator on Riemannian Spin Manifolds

2019 ◽  
Vol 370 (3) ◽  
pp. 853-871
Author(s):  
Yasushi Homma ◽  
Uwe Semmelmann
Keyword(s):  
Spin Manifolds

scholarly journals On Gromov’s conjecture for totally non-spin manifolds

2016 ◽  
Vol 08 (04) ◽  
pp. 571-587
Author(s):  
Dmitry Bolotov ◽  
Alexander Dranishnikov
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Universal Covering ◽  
Positive Scalar Curvature ◽  
Fundamental Groups ◽  
Closed Formula ◽  
Duality Group ◽  
Positive Scalar ◽  
Spin Manifolds ◽  
Stability Conjecture

Gromov’s conjecture states that for a closed [Formula: see text]-manifold [Formula: see text] with positive scalar curvature, the macroscopic dimension of its universal covering [Formula: see text] satisfies the inequality [Formula: see text] [9]. We prove that for totally non-spin [Formula: see text]-manifolds, the inequality [Formula: see text] implies the inequality [Formula: see text]. This implication together with the main result of [6] allows us to prove Gromov’s conjecture for totally non-spin [Formula: see text]-manifolds whose fundamental group is a virtual duality group with [Formula: see text]. In the case of virtually abelian groups, we reduce Gromov’s conjecture for totally non-spin manifolds to the problem whether [Formula: see text]. This problem can be further reduced to the [Formula: see text]-stability conjecture for manifolds with free abelian fundamental groups.

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