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A spectral sequence for orbifold cobordism

Andrés Ángel (2009)

Banach Center Publications

The aim of this paper is to introduce a spectral sequence that converges to the cobordism groups of orbifolds with given isotropy representations. In good cases the E¹-term of this spectral sequence is given by a certain cobordism group of orbibundles over purely ineffective orbifolds which can be identified with the bordism group of the classifying space of the Weyl group of a finite subgroup of O(n). We use this spectral sequence to calculate some cobordism groups of orbifolds for low dimensions,...

h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness

Mady Demdah Kartoue (2011)

Annales de l’institut Fourier

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation.One aspect of...

Non-slice linear combinations of algebraic knots

Matthew Hedden, Paul Kirk, Charles Livingston (2012)

Journal of the European Mathematical Society

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.

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