Paclitaxel, Topotecan, and Cisplatin in Treating Patients With Advanced, Persistent, or Recurrent Cervical Cancer

DISEASE CHARACTERISTICS: * Advanced, persistent, or recurrent squamous or nonsquamous cell carcinoma of the cervix with documented disease progression * Histologic confirmation of the original primary tumor is required * Disease must be measurable in at least one dimension by conventional techniques, including palpation, plain x-ray, CT scan, or MRI * Measurable disease is defined as at least one lesion that can be accurately measured * Each lesion must be ≥ 20 mm by conventional techniques or ≥ 10 mm by spiral CT scan * Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence ≥ 90 days after completion of radiation therapy PATIENT CHARACTERISTICS: * GOG performance status 0-2 * Platelet count ≥ 100,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Creatinine ≤ 1.5 times upper limit of normal (ULN) * Bilirubin ≤ 1.5 times ULN * SGOT and alkaline phosphatase ≤ 2.5 times ULN * Neuropathy (sensory and motor) ≤ grade 1 * No active infection requiring antibiotics * No evidence of more than one malignancy present within the past 5 years * Nonmelanoma skin cancer allowed * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: * No prior therapy with cytotoxic drugs for advanced or recurrent cervical carcinoma * Prior cisplatin as a radiosensitizer for primary treatment of disease allowed * No previous cancer treatment that contraindicates study treatment * No prior radiotherapy to any portion of the abdominal cavity or pelvis except for the treatment of cervical cancer * No prior chemotherapy for any abdominal or pelvic tumor except for the treatment of cervical cancer * Recovered from effects of recent surgery, radiotherapy, or other therapy * At least 4 weeks since prior radiotherapy * More than 3 years since prior radiotherapy for localized cancer of the breast, head and neck, or skin and free of recurrent or metastatic disease * More than 3 years since prior adjuvant chemotherapy for localized breast cancer provided patient is free of recurrent or metastatic disease * No hormonal therapy directed at the malignant tumor within the past week * Concurrent hormone replacement therapy is permitted * No concurrent amifostine or other protective reagents