Knots and shellable cell partitionings of $S^{3}$

On Property I for Knots in S3

This paper deals with the question of which knot surgeries on S3 can yield 3-manifolds homeomorphic to, or with the same fundamental group as, the Poincart homology 3-sphere.

Knots in S3 and Bordered Heegaard Floer Homology

Acknowledgements 1

Non-triviality of the A-polynomial for Knots in S3

The A-polynomial of a knot in S3 is a complex plane curve associated to the set of representations of the fundamental group of the knot exterior into SL2C. Here, we show that a non-trivial knot in S3 has a non-trivial A-polynomial. We deduce this from the gauge-theoretic work of Kronheimer and Mrowka on SU2-representations of Dehn surgeries on knots in S3. As a corollary, we show that if a conj...

Criterions for Shellable Multicomplexes

After [4] the shellability of multicomplexes Γ is given in terms of some special faces of Γ called facets. Here we give a criterion for the shellability in terms of maximal facets. Multigraded pretty clean filtration is the algebraic counterpart of a shellable multicomplex. We give also a criterion for the existence of a multigraded pretty clean filtration.

On Rectangular Partitionings in