Intersection operations for measured laminations carried by a branched manifold

Ulrich Oertel; Athanase Papadopoulos

doi:10.1016/0166-8641(93)90015-6

Intersection operations for measured laminations carried by a branched manifold

Ulrich Oertel, Athanase Papadopoulos

Rutgers Newark, Math & Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We described an algebraic intersection operation for measured laminations carried by a codimension-1 branched manifold embedded in a manifold. Using this operation we define real-valued intersection forms and obtain formulas for their values in terms of invariant measures on the branched manifolds. Finally, we use the intersection operation to define a multiple-valued intersection "operation" for isotopy classes of incompressible surfaces in a Haken manifold.

Original language	English (US)
Pages (from-to)	99-116
Number of pages	18
Journal	Topology and its Applications
Volume	50
Issue number	2
DOIs	https://doi.org/10.1016/0166-8641(93)90015-6
State	Published - Apr 27 1993

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Branched manifold
Haken manifold
incompressible surface
intersection
measured lamination
surface

Access to Document

10.1016/0166-8641(93)90015-6

Fingerprint Dive into the research topics of 'Intersection operations for measured laminations carried by a branched manifold'. Together they form a unique fingerprint.

Cite this

@article{e38a994e5efb432b9c3c192f5d2b862d,

title = "Intersection operations for measured laminations carried by a branched manifold",

abstract = "We described an algebraic intersection operation for measured laminations carried by a codimension-1 branched manifold embedded in a manifold. Using this operation we define real-valued intersection forms and obtain formulas for their values in terms of invariant measures on the branched manifolds. Finally, we use the intersection operation to define a multiple-valued intersection {"}operation{"} for isotopy classes of incompressible surfaces in a Haken manifold.",

keywords = "Branched manifold, Haken manifold, incompressible surface, intersection, measured lamination, surface",

author = "Ulrich Oertel and Athanase Papadopoulos",

year = "1993",

month = apr,

day = "27",

doi = "10.1016/0166-8641(93)90015-6",

language = "English (US)",

volume = "50",

pages = "99--116",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Intersection operations for measured laminations carried by a branched manifold

AU - Oertel, Ulrich

AU - Papadopoulos, Athanase

PY - 1993/4/27

Y1 - 1993/4/27

N2 - We described an algebraic intersection operation for measured laminations carried by a codimension-1 branched manifold embedded in a manifold. Using this operation we define real-valued intersection forms and obtain formulas for their values in terms of invariant measures on the branched manifolds. Finally, we use the intersection operation to define a multiple-valued intersection "operation" for isotopy classes of incompressible surfaces in a Haken manifold.

AB - We described an algebraic intersection operation for measured laminations carried by a codimension-1 branched manifold embedded in a manifold. Using this operation we define real-valued intersection forms and obtain formulas for their values in terms of invariant measures on the branched manifolds. Finally, we use the intersection operation to define a multiple-valued intersection "operation" for isotopy classes of incompressible surfaces in a Haken manifold.

KW - Branched manifold

KW - Haken manifold

KW - incompressible surface

KW - intersection

KW - measured lamination

KW - surface

UR - http://www.scopus.com/inward/record.url?scp=43949171485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949171485&partnerID=8YFLogxK

U2 - 10.1016/0166-8641(93)90015-6

DO - 10.1016/0166-8641(93)90015-6

M3 - Article

AN - SCOPUS:43949171485

VL - 50

SP - 99

EP - 116

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -