Splitting (complicated) surfaces is hard. Chambers, E. W., de Verdière, É. C., Erickson, J., Lazarus, F., & Whittlesey, K. In Proceedings of the 22nd ACM Symposium on Computational Geometry, Sedona, Arizona, USA, June 5-7, 2006, pages 421--429, 2006.
Splitting (complicated) surfaces is hard [link]Paper  doi  bibtex   
@inproceedings{DBLP:conf/compgeom/ChambersVELW06,
  author    = {Erin W. Chambers and
               {\'{E}}ric Colin de Verdi{\`{e}}re and
               Jeff Erickson and
               Francis Lazarus and
               Kim Whittlesey},
  title     = {Splitting (complicated) surfaces is hard},
  booktitle = {Proceedings of the 22nd {ACM} Symposium on Computational Geometry,
               Sedona, Arizona, USA, June 5-7, 2006},
  pages     = {421--429},
  year      = {2006},
  crossref  = {DBLP:conf/compgeom/2006},
  url       = {http://doi.acm.org/10.1145/1137856.1137918},
  doi       = {10.1145/1137856.1137918},
  timestamp = {Tue, 21 Nov 2017 00:00:00 +0100},
  biburl    = {https://dblp.org/rec/bib/conf/compgeom/ChambersVELW06},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}
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