The homotopy groups of a homotopy group completion

If you need an accessible version of this item, please email your request to digschol@iu.edu so that they may create one and provide it to you.
Date
2019
Language
English
Embargo Lift Date
Committee Members
Degree
Degree Year
Department
Grantor
Journal Title
Journal ISSN
Volume Title
Found At
Springer
Abstract

Let M be a topological monoid with homotopy group completion ΩBM. Under a strong homotopy commutativity hypothesis on M, we show that πk(ΩBM) is the quotient of the monoid of free homotopy classes [Sk, M] by its submonoid of nullhomotopic maps.

We give two applications. First, this result gives a concrete description of the Lawson homology of a complex projective variety in terms of pointwise addition of spherical families of effective algebraic cycles. Second, we apply this result to monoids built from the unitary, or general linear, representation spaces of discrete groups, leading to results about lifting continuous families of characters to continuous families of representations.

Description
item.page.description.tableofcontents
item.page.relation.haspart
Cite As
Ramras, D. A. (2019). The homotopy groups of a homotopy group completion. Israel Journal of Mathematics, 234(1), 81–124. https://doi.org/10.1007/s11856-019-1914-2
ISSN
Publisher
Series/Report
Sponsorship
Major
Extent
Identifier
Relation
Journal
Israel Journal of Mathematics
Source
ArXiv
Alternative Title
Type
Article
Number
Volume
Conference Dates
Conference Host
Conference Location
Conference Name
Conference Panel
Conference Secretariat Location
Version
Author's manuscript
Full Text Available at
This item is under embargo {{howLong}}