# On genera of polyhedra

Open Mathematics (2012)

- Volume: 10, Issue: 2, page 401-410
- ISSN: 2391-5455

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topYuriy Drozd, and Petro Kolesnyk. "On genera of polyhedra." Open Mathematics 10.2 (2012): 401-410. <http://eudml.org/doc/269672>.

@article{YuriyDrozd2012,

abstract = {We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X p ≅ Y p for all prime p, where X p denotes the image of Xin the localized category S p. We prove that it is equivalent to the stable isomorphism X∨B 0 ≅Y∨B 0, where B 0 is the wedge of all spheres S n such that π nS(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y.},

author = {Yuriy Drozd, Petro Kolesnyk},

journal = {Open Mathematics},

keywords = {Stable homotopy category; Polyhedron; Genus; Cancellation; Orders in semisimple algebras; genera of polyhedra; polyhedron; genus; cancellation; orders in semisimple algebras},

language = {eng},

number = {2},

pages = {401-410},

title = {On genera of polyhedra},

url = {http://eudml.org/doc/269672},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Yuriy Drozd

AU - Petro Kolesnyk

TI - On genera of polyhedra

JO - Open Mathematics

PY - 2012

VL - 10

IS - 2

SP - 401

EP - 410

AB - We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X p ≅ Y p for all prime p, where X p denotes the image of Xin the localized category S p. We prove that it is equivalent to the stable isomorphism X∨B 0 ≅Y∨B 0, where B 0 is the wedge of all spheres S n such that π nS(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y.

LA - eng

KW - Stable homotopy category; Polyhedron; Genus; Cancellation; Orders in semisimple algebras; genera of polyhedra; polyhedron; genus; cancellation; orders in semisimple algebras

UR - http://eudml.org/doc/269672

ER -

## References

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- [9] Switzer R.W., Algebraic Topology - Homotopy and Homology, Grundlehren Math. Wiss., 212, Springer, Berlin-Heidelberg-New York, 1975 Zbl0305.55001

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