The Genus of a Map Hurvitz, Sara
Transactions of the American Mathematical Society,
01/1981, Letnik:
264, Številka:
1
Journal Article
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The elements $\lbrack f' \rbrack(f': X' \rightarrow Y')$ of the genus - $G(f)$ of a map $f: X \rightarrow Y$ are equivalence classes of homotopy classes of maps $f'$ which satisfy: For every prime ...$p$ there exists homotopy equivalences $h_p: X'_p \rightarrow X_p$ and $k_p: Y'_p \rightarrow Y_p$ so that $f_ph_p \sim k_pf'_p$. The genus of $f$ under $X - G^x(f)$ and the genus of $f$ over $Y - G_Y(f)$ are defined similarly. In this paper we prove that under certain conditions on $f$, the sets $G(f), G^x(f)$ and $G_Y(f)$ are finite and admit an abelian group structure. We also compare the genus of $f$ to those of $X$ and $Y$, calculate it for some principal fibrations of the form $K(G, n - 1) \rightarrow X \rightarrow Y$, and deal with the noncancellation phenomenon.
Patients with metastatic triple-negative breast cancer have a poor prognosis. Sacituzumab govitecan is an antibody-drug conjugate composed of an antibody targeting the human trophoblast cell-surface ...antigen 2 (Trop-2), which is expressed in the majority of breast cancers, coupled to SN-38 (topoisomerase I inhibitor) through a proprietary hydrolyzable linker.
In this randomized, phase 3 trial, we evaluated sacituzumab govitecan as compared with single-agent chemotherapy of the physician's choice (eribulin, vinorelbine, capecitabine, or gemcitabine) in patients with relapsed or refractory metastatic triple-negative breast cancer. The primary end point was progression-free survival (as determined by blinded independent central review) among patients without brain metastases.
A total of 468 patients without brain metastases were randomly assigned to receive sacituzumab govitecan (235 patients) or chemotherapy (233 patients). The median age was 54 years; all the patients had previous use of taxanes. The median progression-free survival was 5.6 months (95% confidence interval CI, 4.3 to 6.3; 166 events) with sacituzumab govitecan and 1.7 months (95% CI, 1.5 to 2.6; 150 events) with chemotherapy (hazard ratio for disease progression or death, 0.41; 95% CI, 0.32 to 0.52; P<0.001). The median overall survival was 12.1 months (95% CI, 10.7 to 14.0) with sacituzumab govitecan and 6.7 months (95% CI, 5.8 to 7.7) with chemotherapy (hazard ratio for death, 0.48; 95% CI, 0.38 to 0.59; P<0.001). The percentage of patients with an objective response was 35% with sacituzumab govitecan and 5% with chemotherapy. The incidences of key treatment-related adverse events of grade 3 or higher were neutropenia (51% with sacituzumab govitecan and 33% with chemotherapy), leukopenia (10% and 5%), diarrhea (10% and <1%), anemia (8% and 5%), and febrile neutropenia (6% and 2%). There were three deaths owing to adverse events in each group; no deaths were considered to be related to sacituzumab govitecan treatment.
Progression-free and overall survival were significantly longer with sacituzumab govitecan than with single-agent chemotherapy among patients with metastatic triple-negative breast cancer. Myelosuppression and diarrhea were more frequent with sacituzumab govitecan. (Funded by Immunomedics; ASCENT ClinicalTrials.gov number, NCT02574455; EudraCT number, 2017-003019-21.).
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