Mnthletodjxy. Somereason y as for 5 gnstht 5 ±

" %, . )1 or

0h "oK) ).

. Gsidr Uh) aoty on the unit sphe 5 "

in ¢ ? Then the Both subsp f the north plc D the snbgp

{ Mott : meant } ± NNH,

so 5¥ Nut ,

Spats .

s÷ "%) ="KB ± ND

.

Emily ,5¥ 54%1

. ,) .

speed Ge : 5 ± * "ku) =su % I sub

.4P

"

= { ( xo, . ,

xD tenth{ 8#helxo, . ,

xD ~X( xo , . , xn ) t tee .

= { (% ,.

,xD e 5 "

}/~ . the 1%, . ,

xD ~Xk° . -xD vxts

'

.

sun +1 ) wb on 5 " " & poses the guide doses,

so it ads Hrsilnf) an FP ?

Isotropy subsp for, sg 10 : . "

:O :D EFP "

is just

{ (Mohan,) : Menk 'B± Ulnl

,so EPE sun "kh ) .

Notice Hit,

since SND ± WYND,

uhetht apnea "hh , ± ( snhtkunkn, ± 51ns,

giving a fikslih na ) as 5h '

: on

When nil,

th > giy Ua ) - 53 The WH np 5 → 5 is better hmm as the Hopf fibakh.

:P ' Is'

For n > 1

,the fibnks s

'as 5+1

→ ¢P'

one gennlzd Hpf fibrths

. ht Sph ) be the spplokgrap,

i.e.,the subsp f 6L (n ,

IH) tht puns the quetminr inner psht on IH"

;

qnwmty ,the subsp f obnb Me Suk ) st . M%M=r

,the r=#n±f ) .

them SplintDubtmsitwf an 5h +3EIH

" "& posers qmtrninr lines

,so ub a IHIP?

The Ddpysnbgpf a port in IHIP"

is no .to Spl D,

so

IHPE s*'%pu)xspH)

Nn,5↳3EsPh%h ) ,

so we see Hit IHIPE s"

"¥pcD.

She Spa) = 5,this Sis wk genial

Hptfibmkh s3↳5→ - IHP ? Sine IHP'

I 54,

neat th quid are s3s5→s4.

the tsatt be I me Hpf flanks : 5 as s's

→ Ss ± OR,

but the

non - usoritvib f the admins put you K bey . bhp defe Op" far n >

2.4 it ts art tht,

am thkyh 04 " exist,the no fbnlm 5- 53ns Op ?