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According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem.
Yoshihiro Hirato, and Masamichi Takase. "Compositions of equi-dimensional fold maps." Fundamenta Mathematicae 216.2 (2012): 119-128. <http://eudml.org/doc/282606>.
@article{YoshihiroHirato2012, abstract = {According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem.}, author = {Yoshihiro Hirato, Masamichi Takase}, journal = {Fundamenta Mathematicae}, keywords = {fold map; Toda bracket; composition; stable homotopy group; bordism}, language = {eng}, number = {2}, pages = {119-128}, title = {Compositions of equi-dimensional fold maps}, url = {http://eudml.org/doc/282606}, volume = {216}, year = {2012}, }
TY - JOUR AU - Yoshihiro Hirato AU - Masamichi Takase TI - Compositions of equi-dimensional fold maps JO - Fundamenta Mathematicae PY - 2012 VL - 216 IS - 2 SP - 119 EP - 128 AB - According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem. LA - eng KW - fold map; Toda bracket; composition; stable homotopy group; bordism UR - http://eudml.org/doc/282606 ER -