Immersions of Non-orientable Surfaces
| dc.creator | Nowik, Tahl | |
| dc.date | 2003-10-02 | |
| dc.date.accessioned | 2026-07-07T05:01:35Z | |
| dc.date.available | 2026-07-07T05:01:35Z | |
| dc.description | Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R^3, with values in any Abelian group. We show they are all functions of the universal order 1 invariant that we construct as T \oplus P \oplus Q where T is a Z valued invariant reflecting the number of triple points of the immersion, and P,Q are Z/2 valued invariants characterized by the property that for any regularly homotopic immersions i,j:F\to R^3, P(i)-P(j) \in Z/2 (respectively Q(i)-Q(j) \in Z/2) is the number mod 2 of tangency points (respectively quadruple points) occurring in any generic regular homotopy between i and j. For immersion i:F\to R^3 and diffeomorphism h:F\to F such that i and i \circ h are regularly homotopic we show: P(i\circ h)-P(i) = Q(i\circ h)-Q(i) = (rank(h_* - Id) + E(\det h_**)) mod 2 where h_* is the map induced by h on H_1(F;Z/2), h_** is the map induced by h on H_1(F;Q) (Q=the rationals), and for 0 \neq q \in Q, E(q) \in Z/2 is 0 or 1 according to whether q is positive or negative, respectively. | |
| dc.identifier | https://arxiv.org/abs/math/0310025 | |
| dc.identifier | http://arxiv.org/abs/math/0310025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68725 | |
| dc.subject | Geometric Topology | |
| dc.title | Immersions of Non-orientable Surfaces | |
| dc.type | text |