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Realizations of countable groups as fundamental groups of compactaVirk, Žiga, 1982-Vprašanje o realizaciji končnih grup v obliki fundamentalnih grup kompaktnih metričnih prostorov je bilo dolgo časa odprto. Take realizacije je razmeroma lahko konstruirati v okviru metričnih ali ... kompaktnih prostorov. Kombinacija obeh lastnosti pa je za fundamentalno grupo zelo restriktivna. Problem so obravnavali mnogi topologi (vključno s Cannonom in Connerjem) vendar do rešitve niso prišli. V tem članku dokažemo, da je možno vsako končno grupo realizirati kot fundamentalno grupo kompaktnega podprostora v ▫${\mathbb R}^4$▫. V skladu z izrekom Shelaha [S. Shelah, Can the Fundamental (Homotopy) Group of a Space be the Rationals?, Proc. Amer. Math. Soc. 103, no. 2, (1988), 627-632] omenjeni prostori niso lokalno s potmi povezani, če grupa ni končno predstavljiva. Izrek je dokazan z eksplicitno konstrukcijo prostora ▫$X_G$▫ za vsako števno grupo ▫$G$▫.Source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 10, no. 3, 2013, str. 1573-1589)Type of material - article, component partPublish date - 2013Language - englishCOBISS.SI-ID - 16654681
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source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 10, no. 3, 2013, str. 1573-1589)
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Virk, Žiga, 1982- | 26522 |
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