Homology of spaces of directed paths in euclidean pattern spaces

Roy Meshulam; Martin Raussen

doi:10.1007/978-3-319-44479-6_24

Homology of spaces of directed paths in euclidean pattern spaces

Roy Meshulam, Martin Raussen

Mathematics

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Let F be a family of subsets of {1,…, n} and let (formula presented) Let X_F=R_n\Y_F. For a vector of positive integers k = (k1,…, k n) let P(X_F)^k+1₀ denote the space of monotone paths from 0 = (0,…,0) to k + 1 = (k1 + 1,…, k_n + 1) whose interior is contained in X_F. The path spaces P(X_F)^k+1₀ appear as natural examples in the study of Dijkstra’s PV-model for parallel computations in concurrency theory. We study the topology of P(X_F)^k+1₀ by relating it to a subspace arrangement in a product of simplices. This, in particular, leads to a computation of the homology of P(X_F)k+10 in terms of certain order complexes associated with the hypergraph F.

Original language	English
Title of host publication	A Journey through Discrete Mathematics
Subtitle of host publication	A Tribute to Jiri Matousek
Pages	593-614
Number of pages	22
ISBN (Electronic)	9783319444796
DOIs	https://doi.org/10.1007/978-3-319-44479-6_24
State	Published - 1 Jan 2017

All Science Journal Classification (ASJC) codes

Economics, Econometrics and Finance(all)
General Computer Science
General Business,Management and Accounting
General Mathematics

Access to Document

10.1007/978-3-319-44479-6_24

Cite this

@inbook{4bf2e30d7aea4cc3b5da87e1d91d6072,

title = "Homology of spaces of directed paths in euclidean pattern spaces",

abstract = "Let F be a family of subsets of \{1,…, n\} and let (formula presented) Let XF=Rn\textbackslash{}YF. For a vector of positive integers k = (k1,…, k n) let P(XF)k+10 denote the space of monotone paths from 0 = (0,…,0) to k + 1 = (k1 + 1,…, kn + 1) whose interior is contained in XF. The path spaces P(XF)k+10 appear as natural examples in the study of Dijkstra{\textquoteright}s PV-model for parallel computations in concurrency theory. We study the topology of P(XF)k+10 by relating it to a subspace arrangement in a product of simplices. This, in particular, leads to a computation of the homology of P(XF)k+10 in terms of certain order complexes associated with the hypergraph F.",

author = "Roy Meshulam and Martin Raussen",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-44479-6\_24",

language = "الإنجليزيّة",

isbn = "9783319444789",

pages = "593--614",

booktitle = "A Journey through Discrete Mathematics",

}

TY - CHAP

T1 - Homology of spaces of directed paths in euclidean pattern spaces

AU - Meshulam, Roy

AU - Raussen, Martin

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let F be a family of subsets of {1,…, n} and let (formula presented) Let XF=Rn\YF. For a vector of positive integers k = (k1,…, k n) let P(XF)k+10 denote the space of monotone paths from 0 = (0,…,0) to k + 1 = (k1 + 1,…, kn + 1) whose interior is contained in XF. The path spaces P(XF)k+10 appear as natural examples in the study of Dijkstra’s PV-model for parallel computations in concurrency theory. We study the topology of P(XF)k+10 by relating it to a subspace arrangement in a product of simplices. This, in particular, leads to a computation of the homology of P(XF)k+10 in terms of certain order complexes associated with the hypergraph F.

AB - Let F be a family of subsets of {1,…, n} and let (formula presented) Let XF=Rn\YF. For a vector of positive integers k = (k1,…, k n) let P(XF)k+10 denote the space of monotone paths from 0 = (0,…,0) to k + 1 = (k1 + 1,…, kn + 1) whose interior is contained in XF. The path spaces P(XF)k+10 appear as natural examples in the study of Dijkstra’s PV-model for parallel computations in concurrency theory. We study the topology of P(XF)k+10 by relating it to a subspace arrangement in a product of simplices. This, in particular, leads to a computation of the homology of P(XF)k+10 in terms of certain order complexes associated with the hypergraph F.

UR - http://www.scopus.com/inward/record.url?scp=85042457615&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-44479-6_24

DO - 10.1007/978-3-319-44479-6_24

M3 - فصل

SN - 9783319444789

SP - 593

EP - 614

BT - A Journey through Discrete Mathematics

ER -

Homology of spaces of directed paths in euclidean pattern spaces

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this