Topological invariance of the milnor number mod 2

Topological Invariants of Real Milnor Fibres

Let F : (R,0)→(R,0) and g : (R,0)→R be analytic germs, let Br ⊂ R be a closed ball of small radius centred at the origin, and let Wz = F −1(z) ∩ Br. Let λ(g;Wz) = ∑ p(−1), where λ(p) is the Morse index at a critical point p of a Morse function which approximates g|Wz. For F and g satisfying some natural assumptions, we shall show that there is a finite family of analytic germs θi(z) such that λ...

Milnor Number of Weighted-Lê–Yomdin Singularities

Invariance of Milnor Numbers and Topology of Complex Polynomials

We give a global version of Lê-Ramanujam μ-constant theorem for polynomials. Let (ft), t ∈ [0, 1], be a family of polynomials of n complex variables with isolated singularities, whose coefficients are polynomials in t. We consider the case where some numerical invariants are constant (the affine Milnor number μ(t), the Milnor number at infinity λ(t), the number of critical values, the number of...

2 00 2 Topological charge and topological susceptibility in connection with translation and gauge invariance

It is shown that the evaluation of the expectation value (EV) of topological charge density over θ-vacuum is reduced to investigation of the Chern-Simons term EV. An equation for this quantity is established and solved. EV of the topological charge density at an arbitrary θ occurs equal to zero and, as a consequence, topological susceptibility of both QCD and pure Yang-Mills vacua defined in a ...

Topological Invariance of the Witten Index

We discuss the Witten index in terms of Krein's spectral shift function, and prove invariance of the Witten index under suitable relative trace class hypotheses.