### Abstract

Original language | English |
---|---|

Pages (from-to) | 801-805 |

Number of pages | 5 |

Journal | Osaka Journal of Mathematics |

Volume | 54 |

Issue number | 4 |

Early online date | 20 Oct 2017 |

Publication status | Published - Oct 2017 |

### Fingerprint

### Keywords

- math.AT
- immersions
- cobordism
- inﬁnite loop space
- realizing homology classes
- singular maps

### Cite this

*Osaka Journal of Mathematics*,

*54*(4), 801-805.

**Realizing homology classes up to cobordism.** / Grant, Mark; Szűcs, András; Terpai, Tamás.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 54, no. 4, pp. 801-805.

}

TY - JOUR

T1 - Realizing homology classes up to cobordism

AU - Grant, Mark

AU - Szűcs, András

AU - Terpai, Tamás

N1 - Acknowledgements. Szucs and Terpai are supported by the National Research, Development and Innovation Office NKFIH (OTKA) Grant NK 112735 and partially supported by ERC Advanced Grant LDTBud.

PY - 2017/10

Y1 - 2017/10

N2 - It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod 2 homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

AB - It is known that neither immersions nor maps with a fixed finite set of multisingularities are enough to realize all mod 2 homology classes in manifolds. In this paper we define the notion of realizing a homology class up to cobordism; it is shown that for realization in this weaker sense immersions are sufficient, but maps with a fixed finite set of multisingularities are still insufficient.

KW - math.AT

KW - immersions

KW - cobordism

KW - inﬁnite loop space

KW - realizing homology classes

KW - singular maps

M3 - Article

VL - 54

SP - 801

EP - 805

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 4

ER -