Thom series of contact singularities
نویسندگان
چکیده
منابع مشابه
Thom Series of Contact Singularities
Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this...
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We begin with a quick summary of the notions of global singularity theory and the theory of Thom polynomials. For a more detailed review we refer the reader to [1, 15]. Let N and K be two complex manifolds of dimensions n and k respectively; assume that n ≤ k. Consider a holomorphic map f : N → K for which the differential d fp : TpN → TpK at a generic point p ∈ N is nonsingular, i.e. has rank ...
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A contact singularity is a normal singularity (V, 0) together with a holomorphic contact form η on V \ Sing V in a neighbourhood of 0, i.e. η∧(dη) r has no zero, where dim V = 2r + 1. The main result of this paper is that there are no isolated contact singularities.
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Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this paper we show that this is a special case of a product rule. The product rule enables us to calculate the Thom polynomials of singularities if we know the T...
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Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. Let Ω (N, P ) denote an open subspace of J∞(N, P ) which consists of all Boardman submanifolds Σ (N, P ) of symbols J with J ≤ I. An Ω -regular map f : N → P refers to a smooth map having only singularities in Ω (N, P ) and satisfying transversality condition. We will prove what is called the homotopy principle for ...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.176.3.1