Vaccine Therapy, Paclitaxel, and Carboplatin in Treating Patients Who Are Undergoing Surgery for Stage III or Stage IV Ovarian Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

DISEASE CHARACTERISTICS:

* Diagnosis of ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer

  * Stage III or IV disease
* HLA-A1, -A2, and/or -A3 positive
* Must have at least 1 undissected axillary or inguinal lymph node basin
* No recurrent disease

PATIENT CHARACTERISTICS:

* ECOG performance status 0-2
* Hemoglobin ≥ 8.0 g/dL
* WBC \> 3,000/mm\^3
* Absolute neutrophil count \> 1,500/mm\^3
* Hemoglobin A1c \< 7%
* AST and ALT ≤ 2.5 times upper limit of normal (ULN)
* Bilirubin ≤ 2.5 times ULN
* Creatinine ≤ 1.5 times ULN
* HIV negative
* Hepatitis C negative
* No known or suspected allergies to any component of the study vaccine
* No other concurrent malignancy (except for nonmelanoma skin cancer) unless the patient was curatively treated and has been disease free for ≥ 5 years
* No active serious infection
* No autoimmune disorder with visceral involvement
* No prior or active autoimmune disorders requiring cytotoxic or immunosuppressive therapy

  * The following immunologic conditions are allowed:

    * Laboratory evidence of autoimmune disease (e.g., positive antinuclear antibody titer) without symptoms
    * Clinical evidence of vitiligo
    * Other forms of depigmenting illness
    * Mild arthritis requiring NSAIDs
* No New York Heart Association class III or IV heart disease
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No medical contraindication or potential problem that would preclude study compliance

PRIOR CONCURRENT THERAPY:

* At least 2 weeks since prior and no other concurrent chemotherapy, radiotherapy, or immunotherapy (e.g., interferons, tumor necrosis factor, interleukins, or monoclonal antibodies)
* More than 4 weeks since prior and no other concurrent investigational agents
* More than 4 weeks since prior and no concurrent allergy desensitization injections
* More than 4 weeks since prior and no concurrent oral or parenteral systemic corticosteroids
* No prior or concurrent inhaled corticosteroids (e.g., fluticasone and salmetrol, fluticasone, or triamcinolone acetonide)

  * Prior or concurrent topical corticosteroids allowed
* No prior vaccination with MAGE-A1:161-169, FBP:1901-199, Her-2/neu:369-377, MAGE-A1:96-104, or Her-2/neu:754-762
* More than 4 weeks since prior and no concurrent growth factors (e.g., epoetin alfa, darbepoetin alfa, or pegfilgrastim)
* No concurrent treatment for recurrent disease
* No concurrent nitrosoureas
* No concurrent illegal drug use
* Concurrent nonsteroidal anti-inflammatory drugs (NSAIDs), antihistamines, and chronic medications, unless excluded, are allowed
* Short-term therapy for acute conditions not specifically related to ovarian cancer is allowed