State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology

We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map phi. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology....

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Other Authors:	Cochran, Tim D.
Format:	Others
Language:	English
Published:	2011
Subjects:	Mathematics
Online Access:	http://hdl.handle.net/1911/62003

id	ndltd-RICE-oai-scholarship.rice.edu-1911-62003
record_format	oai_dc
spelling	ndltd-RICE-oai-scholarship.rice.edu-1911-620032013-05-01T03:46:37ZState cycles, quasipositive modification, and constructing H-thick knots in Khovanov homologyMathematicsWe study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map phi. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that specific families of such knots cannot be detected by Khovanov's thickness criteria. We also exhibit a sequence of prime links related by quasipositive modification whose width is increasing.Cochran, Tim D.2011-07-25T02:05:09Z2011-07-25T02:05:09Z2010ThesisTextapplication/pdfhttp://hdl.handle.net/1911/62003eng
collection	NDLTD
language	English
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
description	We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map phi. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that specific families of such knots cannot be detected by Khovanov's thickness criteria. We also exhibit a sequence of prime links related by quasipositive modification whose width is increasing.
author2	Cochran, Tim D.
author_facet	Cochran, Tim D.
title	State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
title_short	State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
title_full	State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
title_fullStr	State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
title_full_unstemmed	State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology
title_sort	state cycles, quasipositive modification, and constructing h-thick knots in khovanov homology
publishDate	2011
url	http://hdl.handle.net/1911/62003
_version_	1716584844409962496

State cycles, quasipositive modification, and constructing H-thick knots in Khovanov homology

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