Topological invariance of the homology characters

1930 ◽  
pp. 72-114
Keyword(s):  
Topological Invariance

scholarly journals The Image Milnor Number and Excellent Unfoldings

2021 ◽  
Author(s):  
R Giménez Conejero ◽  
J J Nuño-Ballesteros
Keyword(s):  
Milnor Number ◽  
Basic Properties ◽  
Topological Invariance

Abstract We show three basic properties of the image Milnor number µI(f) of a germ $f\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with isolated instability. First, we show the conservation of the image Milnor number, from which one can deduce the upper semi-continuity and the topological invariance for families. Second, we prove the weak Mond’s conjecture, which states that µI(f) = 0 if and only if f is stable. Finally, we show a conjecture by Houston that any family $f_t\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ with $\mu_I(\,f_t)$ constant is excellent in Gaffney’s sense. For technical reasons, in the last two properties, we consider only the corank 1 case.

scholarly journals A dynamical metric and its ground state from the breaking down of the topological invariance of the Euler characteristic

2019 ◽  
Vol 79 (8) ◽  
Author(s):  
R. Cartas-Fuentevilla ◽  
A. Escalante-Hernández ◽  
A. Herrera-Aguilar ◽  
R. Navarro-Perez
Keyword(s):  
Euler Characteristic ◽  
Ground State ◽  
Topological Invariance

scholarly journals Topological invariance of integral Pontrjagin classes mod p

1995 ◽  
Vol 63 (1) ◽  
pp. 59-67 ◽  
Author(s):  
Banwari Lal Sharma ◽  
Neeta Singh
Keyword(s):  
Topological Invariance ◽  
Mod P

Topological invariance of the Hall conductance and quantization

2015 ◽  
Vol 29 (24) ◽  
pp. 1550135
Author(s):  
Paul Bracken
Keyword(s):  
Chern Class ◽  
Fiber Bundle ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Hall Conductance ◽  
Integer Multiple ◽  
Principal Fiber Bundle ◽  
Topological Invariance ◽  
First Chern Class

It is shown that the Kubo equation for the Hall conductance can be expressed as an integral which implies quantization of the Hall conductance. The integral can be interpreted as the first Chern class of a [Formula: see text] principal fiber bundle on a two-dimensional torus. This accounts for the conductance given as an integer multiple of [Formula: see text]. The formalism can be extended to deduce the fractional conductivity as well.

Superfluidity of the Lattice Anyon Gas

1989 ◽  
Vol 03 (12) ◽  
pp. 1965-1995 ◽  
Author(s):  
Eduardo Fradkin
Keyword(s):  
Quantum Hall ◽  
Goldstone Mode ◽  
Two Dimensional ◽  
Hall Conductance ◽  
Dimensional Lattice ◽  
Quantum Hall Systems ◽  
Wigner Transformation ◽  
Topological Invariance ◽  
Quantum Hall System ◽  
Chern Simons

I consider a gas of “free” anyons with statistical paremeter δ on a two dimensional lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on a lattice coupled to a Chern-Simons gauge theory with coupling [Formula: see text]. I show that if [Formula: see text] and the density [Formula: see text], with r and q integers, the system is a superfluid. If q is even and the system is half filled the state may be either a superfluid or a Quantum Hall System depending on the dynamics. Similar conclusions apply for other values of ρ and δ. The dynamical stability of the Fetter-Hanna-Laughlin goldstone mode is insured by the topological invariance of the quantized Hall conductance of the fermion problem. This leads to the conclusion that anyon gases are generally superfluids or quantum Hall systems.

scholarly journals Topological invariance of the Witten index

1988 ◽  
Vol 79 (1) ◽  
pp. 91-102 ◽  
Author(s):  
F Gesztesy ◽  
B Simon
Keyword(s):  
Witten Index ◽  
Topological Invariance
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