scholarly journals Generalizations of the Nieh-Yan topological invariant

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez
Keyword(s):  
Topological Invariant

Invariants of 3-manifolds derived from universal invariants of framed links

1995 ◽  
Vol 117 (2) ◽  
pp. 259-273 ◽  
Author(s):  
Tomotada Ohtsuki
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Independent Method ◽  
Topological Invariant ◽  
Finite Dimensional

Reshetikhin and Turaev [10] gave a method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra (e.g. a quantum group Uq(sl2)) using finite-dimensional representations of it. In this paper we give another independent method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra via universal invariants of framed links without using representations of the algebra. For Uq(sl2) these two methods give different invariants of 3-manifolds.

A topological invariant for nonlinear rotations of

Nonlinearity ◽  
1997 ◽  
Vol 10 (1) ◽  
pp. 153-158 ◽  
Author(s):  
Elisabeth Pécou
Keyword(s):  
Topological Invariant

scholarly journals A TORSIONAL TOPOLOGICAL INVARIANT

2007 ◽  
Vol 22 (29) ◽  
pp. 5237-5244 ◽  
Author(s):  
H. T. NIEH
Keyword(s):  
Affine Connection ◽  
Euler Class ◽  
Christoffel Symbol ◽  
Space Time ◽  
Topological Invariant ◽  
Point Of View ◽  
Underlying Space ◽  
Recent Developments ◽  
Theory Point ◽  
Curvature And Torsion

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

A new invariant and decompositions of manifolds

2018 ◽  
Vol 27 (02) ◽  
pp. 1850019
Author(s):  
Eiji Ogasa
Keyword(s):  
Topological Invariant ◽  
The Body ◽  
Precise Definition ◽  
Closed Manifold ◽  
Compact Manifolds ◽  
Connected Components ◽  
Fixed Base

We introduce a new topological invariant [Formula: see text] of compact manifolds-with-boundaries [Formula: see text] which is much connected with boundary-unions. A boundary-union is a kind of decomposition of compact manifolds-with-boundaries. See the body of the paper for the precise definition. Let [Formula: see text] and [Formula: see text] be [Formula: see text]-dimensional compact manifolds-with-boundaries. Let [Formula: see text] be a boundary-union of [Formula: see text] and [Formula: see text]. Then we have [Formula: see text] We define [Formula: see text] as follows: First, define an invariant of [Formula: see text]-closed manifolds. Take the maximum of the invariant of all connected-components of the boundary of each handle-body of an ordered-handle-decomposition with a fixed base [Formula: see text], where we impose the condition that the base [Formula: see text] is a (not necessarily connected) closed manifold. Take the minimum of the maximum for all ordered-handle-decompositions with the base [Formula: see text]. It is our another invariant [Formula: see text]. Take the maximum of the minimum, [Formula: see text], for all basis to satisfy the above condition. It is [Formula: see text]. See the body of the paper for the precise definition.

THE DENEF–LOESER ZETA FUNCTION IS NOT A TOPOLOGICAL INVARIANT

2002 ◽  
Vol 65 (01) ◽  
pp. 45-54 ◽  
Author(s):  
E. ARTAL BARTOLO ◽  
P. CASSOU-NOGUÈS ◽  
I. LUENGO ◽  
A. MELLE HERNÁNDEZ
Keyword(s):  
Zeta Function ◽  
Topological Invariant

scholarly journals Topological entropy and partially hyperbolic diffeomorphisms

2008 ◽  
Vol 28 (3) ◽  
pp. 843-862 ◽  
Author(s):  
YONGXIA HUA ◽  
RADU SAGHIN ◽  
ZHIHONG XIA
Keyword(s):  
Topological Entropy ◽  
Topological Invariant ◽  
Compact Manifolds ◽  
Two Dimensional ◽  
One Dimensional ◽  
Hyperbolic Diffeomorphisms ◽  
Lower Semi ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms

AbstractWe consider partially hyperbolic diffeomorphisms on compact manifolds. We define the notion of the unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, we prove the following two results: if the center foliation is one-dimensional, then the topological entropy is locally a constant; and if the center foliation is two-dimensional, then the topological entropy is continuous on the set of all $C^{\infty }$ diffeomorphisms. The proof uses a topological invariant we introduced, Yomdin’s theorem on upper semi-continuity, Katok’s theorem on lower semi-continuity for two-dimensional systems, and a refined Pesin–Ruelle inequality we proved for partially hyperbolic diffeomorphisms.

Sign in / Sign up

Export Citation Format

Share Document