Noncrossing partitions and milnor fibers

Thomas Brady, Michael J Falk, Colum Watt

Research output: Contribution to journalArticle

Abstract

For a finite real reflection group W we use noncrossing partitions of type W to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated W –discriminant ΔW and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the noncrossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of ΔW .

Original languageEnglish (US)
Pages (from-to)3821-3838
Number of pages18
JournalAlgebraic and Geometric Topology
Volume18
Issue number7
DOIs
StatePublished - Dec 11 2018

Fingerprint

Milnor Fiber
Noncrossing Partitions
Cell Complex
Shellability
Reflection Group
Homotopy Type
Homology Groups
Monodromy
Cyclic group
Group Action
Discriminant
Homology
Arrangement
Polynomial
Computing

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Noncrossing partitions and milnor fibers. / Brady, Thomas; Falk, Michael J; Watt, Colum.

In: Algebraic and Geometric Topology, Vol. 18, No. 7, 11.12.2018, p. 3821-3838.

Research output: Contribution to journalArticle

Brady, Thomas ; Falk, Michael J ; Watt, Colum. / Noncrossing partitions and milnor fibers. In: Algebraic and Geometric Topology. 2018 ; Vol. 18, No. 7. pp. 3821-3838.
@article{97aed5e0c1e24a39adf181dfef70f032,
title = "Noncrossing partitions and milnor fibers",
abstract = "For a finite real reflection group W we use noncrossing partitions of type W to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated W –discriminant ΔW and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the noncrossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of ΔW .",
author = "Thomas Brady and Falk, {Michael J} and Colum Watt",
year = "2018",
month = "12",
day = "11",
doi = "10.2140/agt.2018.18.3821",
language = "English (US)",
volume = "18",
pages = "3821--3838",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "7",

}

TY - JOUR

T1 - Noncrossing partitions and milnor fibers

AU - Brady, Thomas

AU - Falk, Michael J

AU - Watt, Colum

PY - 2018/12/11

Y1 - 2018/12/11

N2 - For a finite real reflection group W we use noncrossing partitions of type W to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated W –discriminant ΔW and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the noncrossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of ΔW .

AB - For a finite real reflection group W we use noncrossing partitions of type W to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated W –discriminant ΔW and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the noncrossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of ΔW .

UR - http://www.scopus.com/inward/record.url?scp=85060476047&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060476047&partnerID=8YFLogxK

U2 - 10.2140/agt.2018.18.3821

DO - 10.2140/agt.2018.18.3821

M3 - Article

VL - 18

SP - 3821

EP - 3838

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 7

ER -