2019
Том 71
№ 1

All Issues

Repovš D.

Articles: 2
Article (English)

$S^1$-bott functions on manifolds

Repovš D., Sharko V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1685-1698

We study $S^1$$ -Bott functions on compact smooth manifolds. In particular, we investigate $S_1$-invariant Bott functions on manifolds with circle action.

Article (English)

On the asymptotic extension dimension

Repovš D., Zarichnyi M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 11. - pp. 1523–1530

We introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes the relationship between the asymptotic extensional dimension of a proper metric space and the extension dimension of its Higson corona.