Abstract
Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings
Highlights
Ãîìåîìîðôèçì f, êàê ýòî ëåãêî âûòåêàåò èç ïîñòðîåíèÿ, ïñåâäîàíîñîâñêèé ñ îñîáûìè òî÷êàìè èíâàðèàíòíûõ ñëîåíèé, ïîëó÷àþùèìèñÿ ïðè îòîæäåñòâëåíèè ïåðèîäè÷åñêèõ òî÷åê íà êðàå Π
The covering and the homeomorphism are constructed by means of original mapping
Ãîìåîìîðôèçì f , êàê ýòî ëåãêî âûòåêàåò èç ïîñòðîåíèÿ, ïñåâäîàíîñîâñêèé ñ îñîáûìè òî÷êàìè èíâàðèàíòíûõ ñëîåíèé, ïîëó÷àþùèìèñÿ ïðè îòîæäåñòâëåíèè ïåðèîäè÷åñêèõ òî÷åê íà êðàå Π
Summary
Ëåãêî âèäåòü, ÷òî åñëè èíâàðèàíòíûå ñëîåíèÿ GPA-ãîìåîìîðôèçìà èìåþò õîòÿ áû îäíó îñîáóþ òî÷êó íå÷1⁄4òíîé âàëåíòíîñòè, òî îíè íå ìîãóò áûòü îðèåíòèðóåìûìè. M ýòî òàêîå íåïðåðûâíîå îòîáðàæåíèå p íåêîòîðîé ïîâåðõíîñòè M íà M , ÷òî äëÿ êàæäîé òî÷êè x ∈/ Σ íàéä1⁄4òñÿ îòêðûòûé äèñê U ∋ x , äëÿ êîòîðîãî p−1(U ) åñòü îáúåäèíåíèå k íåïåðåñåêàþùèõñÿ äèñêîâ U∑1, .
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