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Equivariant Weiss Calculus and Loop ...

Tynan, Philip Douglas.

Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds./
Author:	Tynan, Philip Douglas.
Description:	1 online resource (58 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355029703

Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds.
Tynan, Philip Douglas.

Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds. - 1 online resource (58 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)--Harvard University, 2016.

Includes bibliographical references

In the mid 1980s, Steve Mitchell and Bill Richter produced a filtration of the Stiefel manifolds O(V; W) and U(V; W) of orthogonal and unitary, respectively, maps V → V &oplus; W stably split as a wedge sum of Thom spaces defined over Grassmanians. Additionally, they produced a similar filtration for loops on SU( V), with a similar splitting. A few years later, Michael Crabb made explicit the equivariance of the Stiefel manifold splittings and conjectured that the splitting of the loop space was equivariant as well. However, it has long been unknown whether the loop space of the real Steifel manifold (or even the special case of OSOn) has a similar splitting.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355029703Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds.
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100 1 $a Tynan, Philip Douglas. $3 1193028
245 1 0 $a Equivariant Weiss Calculus and Loop Spaces of Stiefel Manifolds.
264 0 $c 2016
300 $a 1 online resource (58 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Advisers: Michael J. Hopkins; Haynes R. Miller; Jacob A. Lurie.
502 $a Thesis (Ph.D.)--Harvard University, 2016.
504 $a Includes bibliographical references
520 $a In the mid 1980s, Steve Mitchell and Bill Richter produced a filtration of the Stiefel manifolds O(V; W) and U(V; W) of orthogonal and unitary, respectively, maps V → V &oplus; W stably split as a wedge sum of Thom spaces defined over Grassmanians. Additionally, they produced a similar filtration for loops on SU( V), with a similar splitting. A few years later, Michael Crabb made explicit the equivariance of the Stiefel manifold splittings and conjectured that the splitting of the loop space was equivariant as well. However, it has long been unknown whether the loop space of the real Steifel manifold (or even the special case of OSOn) has a similar splitting.
520 $a Here, inspired by the work of Greg Arone that made use of Weiss' orthogonal calculus to generalize the results of Mitchell and Richter, we obtain an Z/2Z-equivariant splitting theorem using an equivariant version of Weiss calculus. In particular, we show that OU( V; W) has an equivariant stable splitting when dim W > 0. By considering the (geometric) fixed points of this loop space, we also obtain, as a corollary, a stable splitting of the space O(U( V; W),O(VR;W R)) of paths in U(V; W) from I to a point of O(VR;W R) as well. In particular, by setting W = C, this gives us a stable splitting of O(SU n / SOn).
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Harvard University. $b Mathematics. $3 1193029
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10632870 $z click for full text (PQDT)

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