id sid tid token lemma pos hd76rx9419z 1 1 in in ADP hd76rx9419z 1 2 this this DET hd76rx9419z 1 3 dissertation dissertation NOUN hd76rx9419z 1 4 , , PUNCT hd76rx9419z 1 5 we we PRON hd76rx9419z 1 6 give give VERB hd76rx9419z 1 7 a a DET hd76rx9419z 1 8 new new ADJ hd76rx9419z 1 9 proof proof NOUN hd76rx9419z 1 10 of of ADP hd76rx9419z 1 11 the the DET hd76rx9419z 1 12 main main ADJ hd76rx9419z 1 13 results result NOUN hd76rx9419z 1 14 of of ADP hd76rx9419z 1 15 ando ando PROPN hd76rx9419z 1 16 , , PUNCT hd76rx9419z 1 17 hopkins hopkin NOUN hd76rx9419z 1 18 , , PUNCT hd76rx9419z 1 19 and and CCONJ hd76rx9419z 1 20 strickland strickland INTJ hd76rx9419z 1 21 regarding regard VERB hd76rx9419z 1 22 the the DET hd76rx9419z 1 23 generalized generalized ADJ hd76rx9419z 1 24 homology homology NOUN hd76rx9419z 1 25 of of ADP hd76rx9419z 1 26 the the DET hd76rx9419z 1 27 even even ADV hd76rx9419z 1 28 connective connective ADJ hd76rx9419z 1 29 covers cover NOUN hd76rx9419z 1 30 of of ADP hd76rx9419z 1 31 bu bu PROPN hd76rx9419z 1 32 . . PUNCT hd76rx9419z 2 1 in in ADP hd76rx9419z 2 2 particular particular ADJ hd76rx9419z 2 3 , , PUNCT hd76rx9419z 2 4 we we PRON hd76rx9419z 2 5 prove prove VERB hd76rx9419z 2 6 that that SCONJ hd76rx9419z 2 7 the the DET hd76rx9419z 2 8 so so ADV hd76rx9419z 2 9 - - PUNCT hd76rx9419z 2 10 called call VERB hd76rx9419z 2 11 " " PUNCT hd76rx9419z 2 12 symmetry symmetry NOUN hd76rx9419z 2 13 " " PUNCT hd76rx9419z 2 14 and and CCONJ hd76rx9419z 2 15 " " PUNCT hd76rx9419z 2 16 cocycle cocycle NOUN hd76rx9419z 2 17 " " PUNCT hd76rx9419z 2 18 relations relation NOUN hd76rx9419z 2 19 hold hold VERB hd76rx9419z 2 20 in in ADP hd76rx9419z 2 21 the the DET hd76rx9419z 2 22 e e NOUN hd76rx9419z 2 23 - - NOUN hd76rx9419z 2 24 homology homology NOUN hd76rx9419z 2 25 of of ADP hd76rx9419z 2 26 bu<2k> bu<2k> SPACE hd76rx9419z 2 27 ; ; PUNCT hd76rx9419z 2 28 for for ADP hd76rx9419z 2 29 any any DET hd76rx9419z 2 30 complex complex ADJ hd76rx9419z 2 31 - - PUNCT hd76rx9419z 2 32 orientable orientable ADJ hd76rx9419z 2 33 e e NOUN hd76rx9419z 2 34 and and CCONJ hd76rx9419z 2 35 that that SCONJ hd76rx9419z 2 36 these these DET hd76rx9419z 2 37 relations relation NOUN hd76rx9419z 2 38 are be AUX hd76rx9419z 2 39 the the DET hd76rx9419z 2 40 defining define VERB hd76rx9419z 2 41 relations relation NOUN hd76rx9419z 2 42 whenever whenever SCONJ hd76rx9419z 2 43 e e SYM hd76rx9419z 2 44 = = NOUN hd76rx9419z 2 45 hq hq VERB hd76rx9419z 2 46 or or CCONJ hd76rx9419z 2 47 k=1 k=1 PROPN hd76rx9419z 2 48 , , PUNCT hd76rx9419z 2 49 2 2 NUM hd76rx9419z 2 50 , , PUNCT hd76rx9419z 2 51 or or CCONJ hd76rx9419z 2 52 3 3 X hd76rx9419z 2 53 . . PUNCT hd76rx9419z 3 1 this this DET hd76rx9419z 3 2 new new ADJ hd76rx9419z 3 3 proof proof NOUN hd76rx9419z 3 4 avoids avoid VERB hd76rx9419z 3 5 the the DET hd76rx9419z 3 6 algebro algebro ADJ hd76rx9419z 3 7 - - PUNCT hd76rx9419z 3 8 geometric geometric ADJ hd76rx9419z 3 9 perspective perspective NOUN hd76rx9419z 3 10 of of ADP hd76rx9419z 3 11 ando ando PROPN hd76rx9419z 3 12 , , PUNCT hd76rx9419z 3 13 hopkins hopkin NOUN hd76rx9419z 3 14 , , PUNCT hd76rx9419z 3 15 and and CCONJ hd76rx9419z 3 16 strickland strickland NOUN hd76rx9419z 3 17 and and CCONJ hd76rx9419z 3 18 instead instead ADV hd76rx9419z 3 19 uses use VERB hd76rx9419z 3 20 the the DET hd76rx9419z 3 21 work work NOUN hd76rx9419z 3 22 of of ADP hd76rx9419z 3 23 ravenel ravenel PROPN hd76rx9419z 3 24 , , PUNCT hd76rx9419z 3 25 wilson wilson PROPN hd76rx9419z 3 26 , , PUNCT hd76rx9419z 3 27 and and CCONJ hd76rx9419z 3 28 yagita yagita PROPN hd76rx9419z 3 29 on on ADP hd76rx9419z 3 30 the the DET hd76rx9419z 3 31 unstable unstable ADJ hd76rx9419z 3 32 homology homology NOUN hd76rx9419z 3 33 of of ADP hd76rx9419z 3 34 the the DET hd76rx9419z 3 35 truncated truncate VERB hd76rx9419z 3 36 brown brown ADJ hd76rx9419z 3 37 - - PUNCT hd76rx9419z 3 38 peterson peterson NOUN hd76rx9419z 3 39 spectra spectra NOUN hd76rx9419z 3 40 , , PUNCT hd76rx9419z 3 41 as as ADV hd76rx9419z 3 42 well well ADV hd76rx9419z 3 43 as as ADP hd76rx9419z 3 44 the the DET hd76rx9419z 3 45 relationship relationship NOUN hd76rx9419z 3 46 between between ADP hd76rx9419z 3 47 these these DET hd76rx9419z 3 48 spectra spectra ADJ hd76rx9419z 3 49 and and CCONJ hd76rx9419z 3 50 bu<2k> bu<2k> SPACE hd76rx9419z 3 51 ; ; PUNCT hd76rx9419z 3 52 . . PUNCT hd76rx9419z 4 1 this this DET hd76rx9419z 4 2 approach approach NOUN hd76rx9419z 4 3 allows allow VERB hd76rx9419z 4 4 for for ADP hd76rx9419z 4 5 a a DET hd76rx9419z 4 6 somewhat somewhat ADV hd76rx9419z 4 7 simpler simple ADJ hd76rx9419z 4 8 proof proof NOUN hd76rx9419z 4 9 of of ADP hd76rx9419z 4 10 the the DET hd76rx9419z 4 11 classic classic ADJ hd76rx9419z 4 12 ando ando PROPN hd76rx9419z 4 13 - - PUNCT hd76rx9419z 4 14 hopkins hopkins PROPN hd76rx9419z 4 15 - - PUNCT hd76rx9419z 4 16 strickland strickland NOUN hd76rx9419z 4 17 theorem theorem NOUN hd76rx9419z 4 18 , , PUNCT hd76rx9419z 4 19 clarifies clarify VERB hd76rx9419z 4 20 its its PRON hd76rx9419z 4 21 relation relation NOUN hd76rx9419z 4 22 to to ADP hd76rx9419z 4 23 the the DET hd76rx9419z 4 24 e e NOUN hd76rx9419z 4 25 - - NOUN hd76rx9419z 4 26 homology homology NOUN hd76rx9419z 4 27 hopf hopf NOUN hd76rx9419z 4 28 ring ring NOUN hd76rx9419z 4 29 of of ADP hd76rx9419z 4 30 ku ku PROPN hd76rx9419z 4 31 , , PUNCT hd76rx9419z 4 32 and and CCONJ hd76rx9419z 4 33 shows show VERB hd76rx9419z 4 34 how how SCONJ hd76rx9419z 4 35 it it PRON hd76rx9419z 4 36 fits fit VERB hd76rx9419z 4 37 into into ADP hd76rx9419z 4 38 a a DET hd76rx9419z 4 39 broader broad ADJ hd76rx9419z 4 40 algebraic algebraic ADJ hd76rx9419z 4 41 picture picture NOUN hd76rx9419z 4 42 . . PUNCT