Stabilization of half-skyrmions: Heisenberg spins on a non-simply connected manifold

2002 ◽  
Vol 66 (10) ◽  
Author(s):  
Avadh Saxena ◽  
Rossen Dandoloff
Keyword(s):  
Connected Manifold ◽  
Simply Connected

scholarly journals Yang–Mills theory and jumping curves

2015 ◽  
Vol 26 (05) ◽  
pp. 1550029
Author(s):  
Yasha Savelyev
Keyword(s):  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Chain Complex ◽  
Complex Manifolds ◽  
Smooth Manifolds ◽  
Hermitian Vector Bundle ◽  
Connected Manifold ◽  
Classical Sense ◽  
Yang Mills ◽  
Simply Connected

We study a smooth analogue of jumping curves of a holomorphic vector bundle, and use Yang–Mills theory over S2 to show that any non-trivial, smooth Hermitian vector bundle E over a smooth simply connected manifold, must have such curves. This is used to give new examples complex manifolds for which a non-trivial holomorphic vector bundle must have jumping curves in the classical sense (when c1(E) is zero). We also use this to give a new proof of a theorem of Gromov on the norm of curvature of unitary connections, and make the theorem slightly sharper. Lastly we define a sequence of new non-trivial integer invariants of smooth manifolds, connected to this theory of smooth jumping curves, and make some computations of these invariants. Our methods include an application of the recently developed Morse–Bott chain complex for the Yang–Mills functional over S2.

scholarly journals In simply connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiro Lee Tanaka
Keyword(s):  
Connected Manifold ◽  
Cotangent Bundles ◽  
Lagrangian Cobordisms ◽  
Simply Connected ◽  
Lagrangian Cobordism

Abstract Let Q be a simply connected manifold. We show that every exact Lagrangian cobordism between compact, exact Lagrangians in T*Q is an h-cobordism. This is a corollary of the Abouzaid–Kragh Theorem.

A Note on Involutions with a Finite Number of Fixed Points

1968 ◽  
Vol 20 ◽  
pp. 1522-1530
Author(s):  
John D. Miller
Keyword(s):  
Finite Number ◽  
Fixed Points ◽  
Connected Manifold ◽  
Simply Connected

LetMbe a smooth, closed, simply connected manifold of dimension greater than 5. LetTbe an involution onMwith a positive, finite number of fixed points. Our aim in this paper is to prove the following theorem (which is somewhat like that of Wasserman (7)).

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Grzegorz Graff ◽  
Agnieszka Kaczkowska
Keyword(s):  
Natural Number ◽  
Homotopy Class ◽  
Periodic Points ◽  
Topological Invariant ◽  
Periodic Sequence ◽  
Connected Manifold ◽  
Lefschetz Numbers ◽  
Simply Connected Manifolds ◽  
Simply Connected

AbstractLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

scholarly journals Genus Integration, Abelianization, and Extended Monodromy

2019 ◽  
Author(s):  
Ivan Contreras ◽  
Rui Loja Fernandes
Keyword(s):  
Path Space ◽  
Lie Algebroid ◽  
Connected Manifold ◽  
Arbitrary Genus ◽  
Space Construction ◽  
Monodromy Groups ◽  
Simply Connected

Abstract Given a Lie algebroid we discuss the existence of a smooth abelian integration of its abelianization. We show that the obstructions are related to the extended monodromy groups introduced recently in [9]. We also show that this groupoid can be obtained by a path-space construction, similar to the Weinstein groupoid of [6], but where the underlying homotopies are now supported in surfaces with arbitrary genus. As an application, we show that the prequantization condition for a (possibly non-simply connected) manifold is equivalent to the smoothness of an abelian integration. Our results can be interpreted as a generalization of the classical Hurewicz theorem.

scholarly journals The space of immersed surfaces in a manifold

2013 ◽  
Vol 154 (3) ◽  
pp. 419-438 ◽  
Author(s):  
OSCAR RANDAL–WILLIAMS
Keyword(s):  
Stable Range ◽  
Connected Manifold ◽  
Immersed Surfaces ◽  
Rational Cohomology ◽  
Simply Connected

AbstractWe study the cohomology of the space of immersed genus g surfaces in a simply-connected manifold. We compute the rational cohomology of this space in a stable range which goes to infinity with g. In fact, in this stable range we are also able to obtain information about torsion in the cohomology of this space, as long as we localise away from (g-1).

scholarly journals Diluted planar ferromagnets: nonlinear excitations on a non-simply connected manifold

2004 ◽  
Vol 329 (1-2) ◽  
pp. 155-161 ◽  
Author(s):  
Fagner M. Paula ◽  
Afranio R. Pereira ◽  
Lucas A.S. Mól
Keyword(s):  
Connected Manifold ◽  
Nonlinear Excitations ◽  
Simply Connected

scholarly journals BLACK-HOLE SOLUTION WITHOUT CURVATURE SINGULARITY

2013 ◽  
Vol 28 (30) ◽  
pp. 1350136 ◽  
Author(s):  
F. R. KLINKHAMER
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Spherically Symmetric ◽  
Curvature Singularity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Connected Manifold ◽  
Gravity Effects ◽  
Simply Connected

An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered as a regularization of the Schwarzschild solution over a simply-connected manifold, which has a curvature singularity at the center. Spherically symmetric collapse of matter in ℝ4 may result in this nonsingular black-hole solution, if quantum-gravity effects allow for topology change near the center.

scholarly journals Computable Constants for Korn’s Inequalities on Riemannian Manifolds

2021 ◽  
Author(s):  
R. J. Knops
Keyword(s):  
Boundary Conditions ◽  
Minimal Surface ◽  
Riemannian Manifolds ◽  
Dirichlet Boundary ◽  
Explicit Construction ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Spherical Cap ◽  
Connected Manifold ◽  
Simply Connected

AbstractA method is presented for the explicit construction of the non-dimensional constant occurring in Korn’s inequalities for a bounded two-dimensional Riemannian differentiable simply connected manifold subject to Dirichlet boundary conditions. The method is illustrated by application to the spherical cap and minimal surface.

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