The Structure of the Spin^h Bordism Spectrum
Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We compute the spin$^h$ bordism groups at the prime 2 by proving a structure theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$ as a module over the mod 2 Steenrod algebra. This provides a 2-local spl...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Mills, Keith |
| description | Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We
compute the spin$^h$ bordism groups at the prime 2 by proving a structure
theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$
as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting
of $\mathrm{MSpin}^h$ as a wedge sum of familiar spectra. We also compute the
decomposition of $H^*(\mathrm{MSpin}^h;\mathbb{Z}/2\mathbb{Z})$ explicitly in
degrees up through 30 via a counting process. |
| doi_str_mv | 10.48550/arxiv.2306.17709 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2306_17709</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2306_17709</sourcerecordid><originalsourceid>FETCH-LOGICAL-a679-359bca88281537cec0b048ba6c1041bbc875a176edc4e596ef7d26cccf539d93</originalsourceid><addsrcrecordid>eNotjssOgjAURLtxYdQPcCUfINhS-loq8ZWQuMC1pL2USCJKChj9e0FdTWZyMjkIzQkOIskYXmn3Kp9BSDEPiBBYjdHyfLVe2roO2s5Z71F47TDU5f1y9TYPl5dN1VcLPVJN0ajQt8bO_jlB6W57jg9-ctof43Xiay6UT5kyoKUMJWFUgAVscCSN5kBwRIwBKZgmgtscIssUt4XIQw4ABaMqV3SCFr_Xr21Wu7LS7p0N1tnXmn4Ao2Y8QA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The Structure of the Spin^h Bordism Spectrum</title><source>arXiv.org</source><creator>Mills, Keith</creator><creatorcontrib>Mills, Keith</creatorcontrib><description>Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We
compute the spin$^h$ bordism groups at the prime 2 by proving a structure
theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$
as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting
of $\mathrm{MSpin}^h$ as a wedge sum of familiar spectra. We also compute the
decomposition of $H^*(\mathrm{MSpin}^h;\mathbb{Z}/2\mathbb{Z})$ explicitly in
degrees up through 30 via a counting process.</description><identifier>DOI: 10.48550/arxiv.2306.17709</identifier><language>eng</language><subject>Mathematics - Algebraic Topology</subject><creationdate>2023-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2306.17709$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2306.17709$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Mills, Keith</creatorcontrib><title>The Structure of the Spin^h Bordism Spectrum</title><description>Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We
compute the spin$^h$ bordism groups at the prime 2 by proving a structure
theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$
as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting
of $\mathrm{MSpin}^h$ as a wedge sum of familiar spectra. We also compute the
decomposition of $H^*(\mathrm{MSpin}^h;\mathbb{Z}/2\mathbb{Z})$ explicitly in
degrees up through 30 via a counting process.</description><subject>Mathematics - Algebraic Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjssOgjAURLtxYdQPcCUfINhS-loq8ZWQuMC1pL2USCJKChj9e0FdTWZyMjkIzQkOIskYXmn3Kp9BSDEPiBBYjdHyfLVe2roO2s5Z71F47TDU5f1y9TYPl5dN1VcLPVJN0ajQt8bO_jlB6W57jg9-ctof43Xiay6UT5kyoKUMJWFUgAVscCSN5kBwRIwBKZgmgtscIssUt4XIQw4ABaMqV3SCFr_Xr21Wu7LS7p0N1tnXmn4Ao2Y8QA</recordid><startdate>20230630</startdate><enddate>20230630</enddate><creator>Mills, Keith</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230630</creationdate><title>The Structure of the Spin^h Bordism Spectrum</title><author>Mills, Keith</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-359bca88281537cec0b048ba6c1041bbc875a176edc4e596ef7d26cccf539d93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Algebraic Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Mills, Keith</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Mills, Keith</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Structure of the Spin^h Bordism Spectrum</atitle><date>2023-06-30</date><risdate>2023</risdate><abstract>Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We
compute the spin$^h$ bordism groups at the prime 2 by proving a structure
theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$
as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting
of $\mathrm{MSpin}^h$ as a wedge sum of familiar spectra. We also compute the
decomposition of $H^*(\mathrm{MSpin}^h;\mathbb{Z}/2\mathbb{Z})$ explicitly in
degrees up through 30 via a counting process.</abstract><doi>10.48550/arxiv.2306.17709</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2306.17709 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2306_17709 |
| source | arXiv.org |
| subjects | Mathematics - Algebraic Topology |
| title | The Structure of the Spin^h Bordism Spectrum |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T18%3A11%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Structure%20of%20the%20Spin%5Eh%20Bordism%20Spectrum&rft.au=Mills,%20Keith&rft.date=2023-06-30&rft_id=info:doi/10.48550/arxiv.2306.17709&rft_dat=%3Carxiv_GOX%3E2306_17709%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |