%0 Journal Article %1 romero2010discrete %A Romero, Ana %A Sergeraert, Francis %D 2010 %K algebraic topology %T Discrete Vector Fields and Fundamental Algebraic Topology %U http://arxiv.org/abs/1005.5685 %X We show in this text how the most important homology equivalences of fundamental Algebraic Topology can be obtained as reductions associated to discrete vector fields. Mainly the homology equivalences whose existence -- most often non-constructive -- is proved by the main spectral sequences, the Serre and Eilenberg-Moore spectral sequences. On the contrary, the constructive existence is here systematically looked for and obtained.

@article{romero2010discrete, abstract = {We show in this text how the most important homology equivalences of fundamental Algebraic Topology can be obtained as reductions associated to discrete vector fields. Mainly the homology equivalences whose existence -- most often non-constructive -- is proved by the main spectral sequences, the Serre and Eilenberg-Moore spectral sequences. On the contrary, the constructive existence is here systematically looked for and obtained.}, added-at = {2014-11-18T10:15:22.000+0100}, author = {Romero, Ana and Sergeraert, Francis}, biburl = {https://www.bibsonomy.org/bibtex/2a398925915278f488350a124748e1de3/t.uemura}, description = {Discrete Vector Fields and Fundamental Algebraic Topology}, interhash = {6d9dc7589a66d0a3b91eda953ea1d14d}, intrahash = {a398925915278f488350a124748e1de3}, keywords = {algebraic topology}, note = {cite \href{http://arxiv.org/1005.5685}{arxiv:1005.5685}Comment: 53 pages}, timestamp = {2014-11-18T10:15:22.000+0100}, title = {Discrete Vector Fields and Fundamental Algebraic Topology}, url = {http://arxiv.org/abs/1005.5685}, year = 2010 }