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Chern classes of vector bundles with singular connections

Guiseppe De Cecco (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si fa vedere che alcune classi di Chern di fibrati vettoriali complessi possono essere costruite non solo partendo da connessioni C ma, sotto certe condizioni, anche da connessioni lineari singolari. Nel caso particolare del fibrato tangente possono essere costruite anche a partire da metriche singolari. Viene fatto uso in modo essenziale della L 2 -coomologia di de Rham (introdotta da Cheeger e Teleman).

Chern numbers of a Kupka component

Omegar Calvo-Andrade, Marcio G. Soares (1994)

Annales de l'institut Fourier

We will consider codimension one holomorphic foliations represented by sections ω H 0 ( n , Ω 1 ( k ) ) , and having a compact Kupka component K . We show that the Chern classes of the tangent bundle of K behave like Chern classes of a complete intersection 0 and, as a corollary we prove that K is a complete intersection in some cases.

Chern rank of complex bundle

Bikram Banerjee (2019)

Commentationes Mathematicae Universitatis Carolinae

Motivated by the work of A. C. Naolekar and A. S. Thakur (2014) we introduce notions of upper chern rank and even cup length of a finite connected CW-complex and prove that upper chern rank is a homotopy invariant. It turns out that determination of upper chern rank of a space X sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over X or not. For a closed connected d -dimensional complex manifold we obtain...

Chewing the Khovanov homology of tangles

Magnus Jacobsson (2004)

Fundamenta Mathematicae

We present an elementary description of Khovanov's homology of tangles [K2], in the spirit of Viro's paper [V]. The formulation here is over the polynomial ring ℤ[c], unlike [K2] where the theory was presented over the integers only.

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