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Twisted Homology Operations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Twisted Homology Operations./
作者:	Bernard, Calista.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	136 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-06, Section: B.
Contained By:	Dissertations Abstracts International83-06B.
標題:	Maps. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28688338
ISBN:	9798544203896

Twisted Homology Operations.
Bernard, Calista.

Twisted Homology Operations. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 136 p.

Source: Dissertations Abstracts International, Volume: 83-06, Section: B.

Thesis (Ph.D.)--Stanford University, 2021.

This item must not be sold to any third party vendors.

This thesis develops a theory of operations on the twisted homology of E∞-algebras, generalizing a classical theory developed by J.P. May. First we describe a framework suitable for discussing twisted coefficients, which requires working with E∞-algebras in certain categories of functors. In this context, we define twisted versions of the classical Dyer--Lashof operations, as well as a product. Moreover, we prove that these distinguished operations generate all operations on twisted homology by giving a (non-canonical) explicit basis for the homology of free E∞-algebras in terms of these operations. We also make this statement functorial by proving that the homology of a free E∞-algebra is a free object in an appropriate category of objects equipped with an action of the Dyer--Lashof operations. This theory has applications to the study of E∞-spaces with local coefficients, though these are not discussed in detail here.

ISBN: 9798544203896Subjects--Topical Terms:

544078
Maps.

Twisted Homology Operations.
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520 $a This thesis develops a theory of operations on the twisted homology of E∞-algebras, generalizing a classical theory developed by J.P. May. First we describe a framework suitable for discussing twisted coefficients, which requires working with E∞-algebras in certain categories of functors. In this context, we define twisted versions of the classical Dyer--Lashof operations, as well as a product. Moreover, we prove that these distinguished operations generate all operations on twisted homology by giving a (non-canonical) explicit basis for the homology of free E∞-algebras in terms of these operations. We also make this statement functorial by proving that the homology of a free E∞-algebra is a free object in an appropriate category of objects equipped with an action of the Dyer--Lashof operations. This theory has applications to the study of E∞-spaces with local coefficients, though these are not discussed in detail here.
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