Homologies are infinitely complex

Andras Szucs; Mark Grant

doi:10.12775/TMNA.2015.003

Homologies are infinitely complex

Andras Szucs, Mark Grant

Mathematical Science

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Abstract

We show that for any k>1, stratified sets of finite complexity are insufficient to realize all homology classes of codimension k in all smooth manifolds. We also prove a similar result concerning smooth generic maps whose double-point sets are co-oriented.

Original language	English
Pages (from-to)	55-62
Number of pages	8
Journal	Topological Methods in Nonlinear Analysis
Volume	45
Issue number	1
DOIs	https://doi.org/10.12775/TMNA.2015.003
Publication status	Published - Mar 2015

Keywords

math.AT
55N10
primary 57R95
secondary 57R19
57R45
homology of manifolds
realizing homology classes
Pontryagin-Thom construction for stratified sets
double-point co-oriented maps

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title = "Homologies are infinitely complex",

abstract = "We show that for any k>1, stratified sets of finite complexity are insufficient to realize all homology classes of codimension k in all smooth manifolds. We also prove a similar result concerning smooth generic maps whose double-point sets are co-oriented.",

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author = "Andras Szucs and Mark Grant",

year = "2015",

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doi = "10.12775/TMNA.2015.003",

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AU - Grant, Mark

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KW - math.AT

KW - 55N10

KW - primary 57R95

KW - secondary 57R19

KW - 57R45

KW - homology of manifolds

KW - realizing homology classes

KW - Pontryagin-Thom construction for stratified sets

KW - double-point co-oriented maps

U2 - 10.12775/TMNA.2015.003

DO - 10.12775/TMNA.2015.003

M3 - Article

SN - 1230-3429

VL - 45

SP - 55

EP - 62

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

IS - 1

ER -

Homologies are infinitely complex

Abstract

Keywords

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