id sid tid token lemma pos w3763487k1g 1 1 the the DET w3763487k1g 1 2 space space NOUN w3763487k1g 1 3 of of ADP w3763487k1g 1 4 symplectic symplectic ADJ w3763487k1g 1 5 embeddings embedding NOUN w3763487k1g 1 6 of of ADP w3763487k1g 1 7 ellipsoids ellipsoid NOUN w3763487k1g 1 8 has have AUX w3763487k1g 1 9 been be AUX w3763487k1g 1 10 an an DET w3763487k1g 1 11 object object NOUN w3763487k1g 1 12 of of ADP w3763487k1g 1 13 great great ADJ w3763487k1g 1 14 study study NOUN w3763487k1g 1 15 in in ADP w3763487k1g 1 16 recent recent ADJ w3763487k1g 1 17 years year NOUN w3763487k1g 1 18 . . PUNCT w3763487k1g 2 1 at at ADP w3763487k1g 2 2 this this DET w3763487k1g 2 3 point point NOUN w3763487k1g 2 4 , , PUNCT w3763487k1g 2 5 the the DET w3763487k1g 2 6 existence existence NOUN w3763487k1g 2 7 and and CCONJ w3763487k1g 2 8 isotopy isotopy NOUN w3763487k1g 2 9 properties property NOUN w3763487k1g 2 10 of of ADP w3763487k1g 2 11 this this DET w3763487k1g 2 12 space space NOUN w3763487k1g 2 13 have have AUX w3763487k1g 2 14 been be AUX w3763487k1g 2 15 well well ADV w3763487k1g 2 16 studied study VERB w3763487k1g 2 17 . . PUNCT w3763487k1g 3 1 in in ADP w3763487k1g 3 2 this this DET w3763487k1g 3 3 dissertation dissertation NOUN w3763487k1g 3 4 , , PUNCT w3763487k1g 3 5 we we PRON w3763487k1g 3 6 take take VERB w3763487k1g 3 7 some some DET w3763487k1g 3 8 first first ADJ w3763487k1g 3 9 steps step NOUN w3763487k1g 3 10 toward toward ADP w3763487k1g 3 11 investigating investigate VERB w3763487k1g 3 12 the the DET w3763487k1g 3 13 homotopy homotopy NOUN w3763487k1g 3 14 properties property NOUN w3763487k1g 3 15 of of ADP w3763487k1g 3 16 the the DET w3763487k1g 3 17 space space NOUN w3763487k1g 3 18 of of ADP w3763487k1g 3 19 symplectic symplectic ADJ w3763487k1g 3 20 embeddings embedding NOUN w3763487k1g 3 21 of of ADP w3763487k1g 3 22 ellipsoids ellipsoids PROPN w3763487k1g 3 23 . . PUNCT w3763487k1g 4 1 we we PRON w3763487k1g 4 2 identify identify VERB w3763487k1g 4 3 a a DET w3763487k1g 4 4 loop loop NOUN w3763487k1g 4 5 of of ADP w3763487k1g 4 6 symplectic symplectic ADJ w3763487k1g 4 7 embeddings embedding NOUN w3763487k1g 4 8 e(a e(a PROPN w3763487k1g 4 9 , , PUNCT w3763487k1g 4 10 b b NOUN w3763487k1g 4 11 ) ) PUNCT w3763487k1g 4 12 u u PROPN w3763487k1g 4 13 e(a e(a PROPN w3763487k1g 4 14 , , PUNCT w3763487k1g 4 15 b b PROPN w3763487k1g 4 16 ) ) PUNCT w3763487k1g 4 17 --> --> SPACE w3763487k1g 4 18 ; ; PUNCT w3763487k1g 4 19 b^4(r b^4(r NOUN w3763487k1g 4 20 ) ) PUNCT w3763487k1g 4 21 which which PRON w3763487k1g 4 22 is be AUX w3763487k1g 4 23 contractible contractible ADJ w3763487k1g 4 24 when when SCONJ w3763487k1g 4 25 r r PROPN w3763487k1g 4 26 & & CCONJ w3763487k1g 4 27 gt gt PROPN w3763487k1g 4 28 ; ; PUNCT w3763487k1g 4 29 a+b a+b PUNCT w3763487k1g 4 30 and and CCONJ w3763487k1g 4 31 which which PRON w3763487k1g 4 32 is be AUX w3763487k1g 4 33 non non ADJ w3763487k1g 4 34 - - ADJ w3763487k1g 4 35 contractible contractible ADJ w3763487k1g 4 36 when when SCONJ w3763487k1g 4 37 2a 2a NUM w3763487k1g 4 38 & & CCONJ w3763487k1g 4 39 lt lt PROPN w3763487k1g 4 40 ; ; PUNCT w3763487k1g 4 41 r r PROPN w3763487k1g 4 42 & & CCONJ w3763487k1g 4 43 lt lt PROPN w3763487k1g 4 44 ; ; PUNCT w3763487k1g 4 45 a+b a+b PROPN w3763487k1g 4 46 , , PUNCT w3763487k1g 4 47 provided provide VERB w3763487k1g 4 48 that that SCONJ w3763487k1g 4 49 b b PROPN w3763487k1g 4 50 & & CCONJ w3763487k1g 4 51 lt lt PROPN w3763487k1g 4 52 ; ; PUNCT w3763487k1g 4 53 2a 2a NUM w3763487k1g 4 54 . . PUNCT w3763487k1g 5 1 we we PRON w3763487k1g 5 2 even even ADV w3763487k1g 5 3 show show VERB w3763487k1g 5 4 that that SCONJ w3763487k1g 5 5 this this DET w3763487k1g 5 6 loop loop NOUN w3763487k1g 5 7 is be AUX w3763487k1g 5 8 not not PART w3763487k1g 5 9 homologous homologous ADJ w3763487k1g 5 10 to to ADP w3763487k1g 5 11 a a DET w3763487k1g 5 12 constant constant ADJ w3763487k1g 5 13 map map NOUN w3763487k1g 5 14 in in ADP w3763487k1g 5 15 the the DET w3763487k1g 5 16 given give VERB w3763487k1g 5 17 range range NOUN w3763487k1g 5 18 of of ADP w3763487k1g 5 19 r r NOUN w3763487k1g 5 20 values value NOUN w3763487k1g 5 21 . . PUNCT