A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity

Details A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity

2007-11-28

arxiv.org/abs/0711.4405v2

Mathematics

Geometric Topology

14 pages, 4 figures, fixed two typos

Scientific paper

The Sarkar-Wang algorithm computes the hat version of the Heegaard Floer homology of a closed oriented three manifold. This paper analyzes the computational complexity of the Sarkar-Wang algorithm; then the algorithm is modified to obtain a better bound. Then the computational complexity of calculating HFK hat from a Heegaard diagram by means of the modified Sarkar-Wang algorithm is also analyzed. Under certain assumptions it is shown that the modified Sarkar-Wang algorithm is faster than the Manolescu-Ozsvath-Sarkar algorithm.

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